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Articles 1 - 30 of 44
Full-Text Articles in Discrete Mathematics and Combinatorics
Some Generalizations Of Corona Product Of Two Graphs, Aparajita Borah, Gajendra Pratap Singh
Some Generalizations Of Corona Product Of Two Graphs, Aparajita Borah, Gajendra Pratap Singh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper we are seeking to conceptualize the notion of corona product of two graphs to contrive some special types of graphs. That is, here our attempt is to regenerate a familiar graph as a product graph. We are considering seven familiar graphs here to reconstruct them with the help of corona product of two graphs. Such types of families of the graphs and operations can be used to study biological pathways as well as to find the optimal order and size for the special types of graphs.
The Distinguishing Number Of Some Special Kind Of Graphs, Arti Salat, Amit Sharma
The Distinguishing Number Of Some Special Kind Of Graphs, Arti Salat, Amit Sharma
Applications and Applied Mathematics: An International Journal (AAM)
In the present study, the distinguishing number of some different graphs is examined where different graphs like the coconut tree graph, firecracker graph, jellyfish graph, triangular book graph, and banana tree graph have been taken into account. The major goal of the proposed study is to understand the distinguishing number of different graphs for better insights. It is evident from the results that the distinguishing numbers and automorphism groups of the above-mentioned graphs have been carried out successfully.
(R1979) Permanent Of Toeplitz-Hessenberg Matrices With Generalized Fibonacci And Lucas Entries, Hacène Belbachir, Amine Belkhir, Ihab-Eddine Djellas
(R1979) Permanent Of Toeplitz-Hessenberg Matrices With Generalized Fibonacci And Lucas Entries, Hacène Belbachir, Amine Belkhir, Ihab-Eddine Djellas
Applications and Applied Mathematics: An International Journal (AAM)
In the present paper, we evaluate the permanent and determinant of some Toeplitz-Hessenberg matrices with generalized Fibonacci and generalized Lucas numbers as entries.We develop identities involving sums of products of generalized Fibonacci numbers and generalized Lucas numbers with multinomial coefficients using the matrix structure, and then we present an application of the determinant of such matrices.
(Si10-089) Integer Cordial Labeling Of Alternate Snake Graph And Irregular Snake Graph, Pratik Shah, Dharamvirsinh Parmar
(Si10-089) Integer Cordial Labeling Of Alternate Snake Graph And Irregular Snake Graph, Pratik Shah, Dharamvirsinh Parmar
Applications and Applied Mathematics: An International Journal (AAM)
If a graph G admits integer cordial labeling, it is called an integer cordial graph. In this paper we prove that Alternate m-triangular Snake graph, Quadrilateral Snake graph, Alternate m- quadrilateral Snake graph, Pentagonal Snake graph, Alternate m-pentagonal Snake graph, Irregular triangular Snake graph, Irregular quadrilateral Snake graph, and Irregular pentagonal Snake graphs are integer cordial graphs.
(Si10-054) Nonsplit Edge Geodetic Domination Number Of A Graph, P. Arul Paul Sudhahar, J. Jeba Lisa
(Si10-054) Nonsplit Edge Geodetic Domination Number Of A Graph, P. Arul Paul Sudhahar, J. Jeba Lisa
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we have defined an inventive parameter called the nonsplit edge geodetic domination number of a graph, and some of its general properties are studied. The nonsplit edge geodetic domination number of some standard graph is obtained. In this work, we also determine the realization results of the nonsplit edge geodetic domination number and the edge geodetic number of a graph.
(Si10-130) On Regular Inverse Eccentric Fuzzy Graphs, N. Meenal, J. Jeromi Jovita
(Si10-130) On Regular Inverse Eccentric Fuzzy Graphs, N. Meenal, J. Jeromi Jovita
Applications and Applied Mathematics: An International Journal (AAM)
Two new concepts of regular inverse eccentric fuzzy graphs and totally regular inverse eccentric fuzzy graphs are established in this article. By illustrations, these two graphs are compared and the results are derived. Equivalent condition for the existence of these two graphs are found. The exact values of Order and Size for some standard inverse eccentric graphs are also derived.
Determinant Formulas Of Some Hessenberg Matrices With Jacobsthal Entries, Taras Goy, Mark Shattuck
Determinant Formulas Of Some Hessenberg Matrices With Jacobsthal Entries, Taras Goy, Mark Shattuck
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we evaluate determinants of several families of Hessenberg matrices having various subsequences of the Jacobsthal sequence as their nonzero entries. These identities may be written equivalently as formulas for certain linearly recurrent sequences expressed in terms of sums of products of Jacobsthal numbers with multinomial coefficients. Among the sequences that arise in this way include the Mersenne, Lucas and Jacobsthal-Lucas numbers as well as the squares of the Jacobsthal and Mersenne sequences. These results are extended to Hessenberg determinants involving sequences that are derived from two general families of linear second-order recurrences. Finally, combinatorial proofs are provided …
Logarithmic Mean Labeling Of Some Ladder Related Graphs, A. Durai Baskar
Logarithmic Mean Labeling Of Some Ladder Related Graphs, A. Durai Baskar
Applications and Applied Mathematics: An International Journal (AAM)
In general, the logarithmic mean of two positive integers need not be an integer. Hence, the logarithmic mean is to be an integer; we use either flooring or ceiling function. The logarithmic mean labeling of graphs have been defined in which the edge labels may be assigned by either flooring function or ceiling function. In this, we establish the logarithmic mean labeling on graphs by considering the edge labels obtained only from the flooring function. A logarithmic mean labeling of a graph G with q edges is an injective function from the vertex set of G to 1, 2, 3,..., …
Twin Edge Coloring Of Total Graph And Graphs With Twin Chromatic Index 𝚫+𝟐, S. Anantharaman
Twin Edge Coloring Of Total Graph And Graphs With Twin Chromatic Index 𝚫+𝟐, S. Anantharaman
Applications and Applied Mathematics: An International Journal (AAM)
A twin edge coloring of a graph G is meant a proper edge coloring of G whose colors come from the integers modulo k that induce a proper vertex coloring in which the color of a vertex is the sum of the colors of its incident edges. The minimum k for which G has a twin edge coloring is the twin chromatic index of G. In this paper, I compute twin chromatic index of total graph of path and cycle also construct some special graphs with twin chromatic index is maximum degree plus two.
Q-Sumudu Transforms Pertaining To The Product Of Family Of Q-Polynomials And Generalized Basic Hypergeometric Functions, V. K. Vyas, Ali A. Al –Jarrah, S. D. Purohit
Q-Sumudu Transforms Pertaining To The Product Of Family Of Q-Polynomials And Generalized Basic Hypergeometric Functions, V. K. Vyas, Ali A. Al –Jarrah, S. D. Purohit
Applications and Applied Mathematics: An International Journal (AAM)
The prime objective of commenced article is to determine q-Sumudu transforms of a product of unified family of q-polynomials with basic (or q-) analog of Fox’s H-function and q-analog of I-functions. Specialized cases of the leading outcome are further evaluated as q-Sumudu transform of general class of q-polynomials and q-Sumudu transforms of the basic analogs of Fox’s H-function and I-functions.
The Weak Hyperedge Tenacity Of The Hypercycles, G. H. Shirdel, B. Vaez-Zadeh
The Weak Hyperedge Tenacity Of The Hypercycles, G. H. Shirdel, B. Vaez-Zadeh
Applications and Applied Mathematics: An International Journal (AAM)
Graphs play an important role in our daily life. For example, the urban transport network can be represented by a graph, as the intersections are the vertices and the streets are the edges of the graph. Suppose that some edges of the graph are removed, the question arises how damaged the graph is. There are some criteria for measuring the vulnerability of graph; the tenacity is the best criteria for measuring it. Since the hypergraph generalize the standard graph by defining any edge between multiple vertices instead of only two vertices, the above question is about the hypergraph. When a …
Adjacent Vertex-Distinguishing Proper Edge-Coloring Of Strong Product Of Graphs, S. Anantharaman
Adjacent Vertex-Distinguishing Proper Edge-Coloring Of Strong Product Of Graphs, S. Anantharaman
Applications and Applied Mathematics: An International Journal (AAM)
Let G be a finite, simple, undirected and connected graph. The adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for a proper edge-coloring of G, in which no two adjacent vertices are incident to edges colored with the same set of colors. The minimum number of colors required for an adjacent vertex-distinguishing proper edgecoloring of G is called the adjacent vertex-distinguishing proper edge-chromatic index. In this paper, I compute adjacent vertex-distinguishing proper edge-chromatic index of strong product of graphs.
Adjoint Appell-Euler And First Kind Appell-Bernoulli Polynomials, Pierpaolo Natalini, Paolo E. Ricci
Adjoint Appell-Euler And First Kind Appell-Bernoulli Polynomials, Pierpaolo Natalini, Paolo E. Ricci
Applications and Applied Mathematics: An International Journal (AAM)
The adjunction property, recently introduced for Sheffer polynomial sets, is considered in the case of Appell polynomials. The particular case of adjoint Appell-Euler and Appell-Bernoulli polynomials of the first kind is analyzed.
New Approach Of Deterministic Key Pre-Distribution Scheme Using Triangle Free Quasi Symmetric Designs, Debashis Ghosh, Joydeb Pal
New Approach Of Deterministic Key Pre-Distribution Scheme Using Triangle Free Quasi Symmetric Designs, Debashis Ghosh, Joydeb Pal
Applications and Applied Mathematics: An International Journal (AAM)
A wireless sensor network (WSN) consists of tiny autonomous sensor nodes with some constraints. There are organizations having moderately necessitates of these kind of networks. So, security become an indispensable concern in WSN, due to potential adversaries. To overcome the security problem, keys are pre-loaded to the nodes before deployment. Among all key distribution schemes, deterministic key pre-distribution scheme (KPS) using combinatorial design is efficient regarding security aspect. In this paper, a deterministic approach, based on combinatorial design, for key assignment before the network deployment has been presented. Here the quasi-symmetric design which is of triangle-free is being used to …
Simplifying Coefficients In A Family Of Ordinary Differential Equations Related To The Generating Function Of The Laguerre Polynomials, Feng Qi
Applications and Applied Mathematics: An International Journal (AAM)
In the paper, by virtue of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the Lah inversion formula, the author simplifies coefficients in a family of ordinary differential equations related to the generating function of the Laguerre polynomials.
On B-Chromatic Number Of Prism Graph Families, Nadeem Ansari, R. S. Chandel, Rizwana Jamal
On B-Chromatic Number Of Prism Graph Families, Nadeem Ansari, R. S. Chandel, Rizwana Jamal
Applications and Applied Mathematics: An International Journal (AAM)
A b-coloring of graph 𝐺 is a proper 𝑘-coloring 𝐶 that verifies the following property: for every color class 𝑐𝑖, 1≤𝑖≤𝑘, there exists a vertex 𝑥𝑖, with color 𝑐𝑖, such that all the other colors in 𝐶 are utilized in 𝑥𝑖 neighbors. The b-chromatic number of a graph 𝐺, denoted by 𝜑(𝐺), is the largest integer 𝑘 such that 𝐺 may have a b-coloring by 𝑘 colors. In this paper we discuss the b-coloring of prism graph 𝑌𝑛, central graph of prism graph 𝐶(𝑌𝑛), middle graph of prism graph 𝑀(𝑌𝑛) and the total graph of prism graph 𝑇(𝑌𝑛) and we …
Distance Product Of Graphs, H. S. Mehta, U. P. Acharya
Distance Product Of Graphs, H. S. Mehta, U. P. Acharya
Applications and Applied Mathematics: An International Journal (AAM)
In graph theory, different types of product of two graphs have been studied, e.g. Cartesian product, Tensor product, Strong product, etc. Later on, Cartesian product and Tensor product have been generalized by 2-Cartesian product and 2-Tensor product. In this paper, we give one more generalize form, distance product of two graphs. Mainly we discuss the connectedness, bipartiteness and Eulerian property in this product.
Incomplete Generalized (P; Q; R)-Tribonacci Polynomials, Mark Shattuck, Elif Tan
Incomplete Generalized (P; Q; R)-Tribonacci Polynomials, Mark Shattuck, Elif Tan
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we consider an extension of the tribonacci polynomial, which we will refer to as the generalized (p; q; r)-tribonacci polynomial, denoted by Tn;m(x).We find an explicit formula for Tn;m(x)which we use to introduce the incomplete generalized (p; q; r)-tribonacci polynomials and derive several properties. An explicit formula for the generating function of the incomplete generalized polynomials is determined and a combinatorial interpretation is provided yielding further identities.
4-Prime Cordiality Of Some Cycle Related Graphs, R. Ponraj, Rajpal Singh, S. S. Narayanan
4-Prime Cordiality Of Some Cycle Related Graphs, R. Ponraj, Rajpal Singh, S. S. Narayanan
Applications and Applied Mathematics: An International Journal (AAM)
Recently three prime cordial labeling behavior of path, cycle, complete graph, wheel, comb, subdivison of a star, bistar, double comb, corona of tree with a vertex, crown, olive tree and other standard graphs were studied. Also four prime cordial labeling behavior of complete graph, book, flower were studied. In this paper, we investigate the four prime cordial labeling behavior of corona of wheel, gear, double cone, helm, closed helm, butterfly graph, and friendship graph.
Private Absorbant Of Generalized De Bruijn Digraphs, B. Johnson
Private Absorbant Of Generalized De Bruijn Digraphs, B. Johnson
Applications and Applied Mathematics: An International Journal (AAM)
No abstract provided.
On Strong Domination Number Of Graphs, S. K. Vaidya, S. H. Karkar
On Strong Domination Number Of Graphs, S. K. Vaidya, S. H. Karkar
Applications and Applied Mathematics: An International Journal (AAM)
A subset S of a vertex set V is called a dominating set of graph G if every vertex of V -S is dominated by some element of set S. If e is an edge with end vertices u and v and degree of u is greater than or equal to degree of v then we say u strongly dominates v. If every vertex of V - S is strongly dominated by some vertex of S then S is called strong dominating set. The minimum cardinality of a strong dominating set is called the strong domination number of graph. We …
Matching Transversal Edge Domination In Graphs, Anwar Alwardi
Matching Transversal Edge Domination In Graphs, Anwar Alwardi
Applications and Applied Mathematics: An International Journal (AAM)
Let G =(V,E) be a graph. A subset X of E is called an edge dominating set of G if every edge in E - X is adjacent to some edge in X . An edge dominating set which intersects every maximum matching inG is called matching transversal edge dominating set. The minimum cardinality of a matching transversal edge dominating set is called the matching transversal edge domination number of G and is denoted by γmt(G). In this paper, we begin an investigation of this parameter.
A Generalized Polynomial Identity Arising From Quantum Mechanics, Shashikant B. Mulay, John J. Quinn, Mark A. Shattuck
A Generalized Polynomial Identity Arising From Quantum Mechanics, Shashikant B. Mulay, John J. Quinn, Mark A. Shattuck
Applications and Applied Mathematics: An International Journal (AAM)
We establish a general identity that expresses a Pfaffian of a certain matrix as a quotient of homogeneous polynomials. This identity arises in the study of weakly interacting many-body systems and its proof provides another way of realizing the equivalence of two proposed types of trial wave functions used to describe such systems. In the proof of our identity, we make use of only elementary linear algebra and combinatorics and thereby avoid use of more advanced conformal field theory in establishing the aforementioned equivalence.
Cobb-Douglas Based Firm Production Model Under Fuzzy Environment And Its Solution Using Geometric Programming, Palash Mandal, Arindam Garai, Tapan K. Roy
Cobb-Douglas Based Firm Production Model Under Fuzzy Environment And Its Solution Using Geometric Programming, Palash Mandal, Arindam Garai, Tapan K. Roy
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we consider Cobb-Douglas production function based model in a firm under fuzzy environment, and its solution technique by making use of geometric programming. A firm may use many finite inputs such as labour, capital, coal, iron etc. to produce one single output. It is well known that the primary intention of using production function is to determine maximum output for any given combination of inputs. Also, the firm may gain competitive advantages if it can buy and sell in any quantities at exogenously given prices, independent of initial production decisions. On the other hand, in reality, constraints …
On Local Asymptotic Stability Of Q-Fractional Nonlinear Dynamical Systems, Ilknur Koca, Elif Demirci
On Local Asymptotic Stability Of Q-Fractional Nonlinear Dynamical Systems, Ilknur Koca, Elif Demirci
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, locally asymptotic stability of q-fractional order nonlinear dynamical systems is introduced and studied. The sufficient conditions for local stability of such dynamical systems are obtained. Also, useful definitions of fractional order q-integrals and q-derivatives are recalled. Finally, a q-fractional order nonlinear dynamical model is considered.
3-Total Super Sum Cordial Labeling By Applying Operations On Some Graphs, Abha Tenguria, Rinku Verma
3-Total Super Sum Cordial Labeling By Applying Operations On Some Graphs, Abha Tenguria, Rinku Verma
Applications and Applied Mathematics: An International Journal (AAM)
The sum cordial labeling is a variant of cordial labeling. In this paper, we investigate 3-Total Super Sum Cordial labeling. This labeling is discussed by applying union operation on some of the graphs. A vertex labeling is assigned as a whole number within the range. For each edge of the graph, assign the label, according to some definite rule, defined for the investigated labeling. Any graph which satisfies 3-Total Super Sum Cordial labeling is known as the 3-Total Super Sum Cordial graphs. Here, we prove that some of the graphs like the union of Cycle and Path graphs, the union …
Independent Domination In Some Wheel Related Graphs, S. K. Vaidya, R. M. Pandit
Independent Domination In Some Wheel Related Graphs, S. K. Vaidya, R. M. Pandit
Applications and Applied Mathematics: An International Journal (AAM)
A set S of vertices in a graph G is called an independent dominating set if S is both independent and dominating. The independent domination number of G is the minimum cardinality of an independent dominating set in G . In this paper, we investigate the exact value of independent domination number for some wheel related graphs.
Domination Integrity Of Line Splitting Graph And Central Graph Of Path, Cycle And Star Graphs, Sultan S. Mahde, Veena Mathad
Domination Integrity Of Line Splitting Graph And Central Graph Of Path, Cycle And Star Graphs, Sultan S. Mahde, Veena Mathad
Applications and Applied Mathematics: An International Journal (AAM)
The domination integrity of a connected graph G = (V (G);E(G)) is denoted as DI(G) and defined by DI(G) = min{|S| + m(G - S)}, where S is a dominating set and m(G-S) is the order of a maximum component of G-S. This paper discusses domination integrity of line splitting graph and central graph of some graphs.
F–Geometric Mean Graphs, A. D. Baskar, S. Arockiaraj
F–Geometric Mean Graphs, A. D. Baskar, S. Arockiaraj
Applications and Applied Mathematics: An International Journal (AAM)
In a study of traffic, the labelling problems in graph theory can be used by considering the crowd at every junction as the weights of a vertex and expected average traffic in each street as the weight of the corresponding edge. If we assume the expected traffic at each street as the arithmetic mean of the weight of the end vertices, that causes mean labelling of the graph. When we consider a geometric mean instead of arithmetic mean in a large population of a city, the rate of growth of traffic in each street will be more accurate. The geometric …
Solution To Some Open Problems On E-Super Vertex Magic Total Labeling Of Graphs, G. Marimuthu, M. S. Raja Durga, G. D. Devi
Solution To Some Open Problems On E-Super Vertex Magic Total Labeling Of Graphs, G. Marimuthu, M. S. Raja Durga, G. D. Devi
Applications and Applied Mathematics: An International Journal (AAM)
Let G be a finite graph with p vertices and q edges. A vertex magic total labeling is a bijection f from V(G)∪E(G) to the consecutive integers 1, 2, ..., p+q with the property that for every u∈V(G) , f( u)+ ∑f(uv)=K for some constant k. Such a labeling is E-super if f :E(G)→{1, 2,..., q}. A graph G is called E-super vertex magic if it admits an E-super vertex magic labeling. In this paper, we solve two open problems given by Marimuthu, Suganya, Kalaivani and Balakrishnan (Marimuthu et al., 2015).