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Full-Text Articles in Discrete Mathematics and Combinatorics

On Local Asymptotic Stability Of Q-Fractional Nonlinear Dynamical Systems, Ilknur Koca, Elif Demirci Jun 2016

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.

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Domination Integrity Of Line Splitting Graph And Central Graph Of Path, Cycle And Star Graphs, Sultan S. Mahde, Veena Mathad Jun 2016

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.

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3-Total Super Sum Cordial Labeling By Applying Operations On Some Graphs, Abha Tenguria, Rinku Verma Jun 2016

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 …

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Independent Monopoly Size In Graphs, Ahmed M. Naji, N. D. Soner Dec 2015

Independent Monopoly Size In Graphs, Ahmed M. Naji, N. D. Soner

Applications and Applied Mathematics: An International Journal (AAM)

In a graph G = (V;E), a set D ⊆V (G) is said to be a monopoly set of G if every vertex v ∈V-D has at least d(v)/ 2 neighbors in D. The monopoly size of G, denoted mo(G), is the minimum cardinality of a monopoly set among all monopoly sets in G. The set D ⊆ V (G) is an independent monopoly set in G if it is both a monopoly set and an independent set in G. The number of vertices in a minimum independent monopoly set in a graph G is the independent monopoly size of …

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F–Geometric Mean Graphs, A. D. Baskar, S. Arockiaraj Dec 2015

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 …

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Solution To Some Open Problems On E-Super Vertex Magic Total Labeling Of Graphs, G. Marimuthu, M. S. Raja Durga, G. D. Devi Dec 2015

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).

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In Honor And Memory Of Professor Lajos Takács, Aliakbar M. Haghighi, Sri G. Mohanty Dec 2015

In Honor And Memory Of Professor Lajos Takács, Aliakbar M. Haghighi, Sri G. Mohanty

Applications and Applied Mathematics: An International Journal (AAM)

This issue of AAM is dedicated to honoring and remembering Professor Lajos Takács. While wrapping up the manuscript of my book (co-authored by Dr. Dimitar Mishev): Delayed and Network Queues, I went back to celebrate his 1962 book, Introduction to the Theory of Queues, where he gives an example illustrating a waiting time paradox, where the waiting time of a passenger waiting for a bus at a bus stop is infinite, while, in reality, he will wait a finite unit of time before a bus arrive. I sent Professor Takács an e-mail on December 4, 2015, inquiring if he had …

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E-Super Vertex Magic Labelling Of Graphs And Some Open Problems, G. Marimuthu, B. Suganya, S. Kalaivani, M. Balakrishnan Jun 2015

E-Super Vertex Magic Labelling Of Graphs And Some Open Problems, G. Marimuthu, B. Suganya, S. Kalaivani, M. Balakrishnan

Applications and Applied Mathematics: An International Journal (AAM)

Let G be a finite graph with p vertices and q edges. A vertex magic total labelling is a bijection from the union of the vertex set and the edge set to the consecutive integers 1, 2, 3, . . . , p + q with the property that for every u in the vertex set, the sum of the label of u and the label of the edges incident with u is equal to k for some constant k. Such a labelling is E-super, if the labels of the edge set is the set {1, 2, 3, . . …

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Combinatorial Identities For Incomplete Tribonacci Polynomials, Mark Shattuck Jun 2015

Combinatorial Identities For Incomplete Tribonacci Polynomials, Mark Shattuck

Applications and Applied Mathematics: An International Journal (AAM)

The incomplete tribonacci polynomials, denoted by Tn(s)(x), generalize the usual tribonacci polynomials Tn (x) and have been shown to satisfy several algebraic identities. In this paper, we provide a combinatorial interpretation for Tn(s)(x) in terms of weighted linear tilings involving three types of tiles. This allows one not only to supply combinatorial proofs of earlier identities for Tn(s)(x) but also to derive new ones. In the final section, we provide a formula for the ordinary generating function of the sequence Tn(s)(x) for a fixed s, as previously …

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Domination Integrity Of Some Path Related Graphs, S. K. Vaidya, N. H. Shah Dec 2014

Domination Integrity Of Some Path Related Graphs, S. K. Vaidya, N. H. Shah

Applications and Applied Mathematics: An International Journal (AAM)

The stability of a communication network is one of the important parameters for network designers and users. A communication network can be considered to be highly vulnerable if the destruction of a few elements cause large damage and only few members are able to communicate. In a communication network several vulnerability measures like binding number, toughness, scattering number, integrity, tenacity, edge tenacity and rupture degree are used to determine the resistance of network to the disruption after the failure of certain nodes (vertices) or communication links (edges). Domination theory also provides a model to measure the vulnerability of a graph …

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Private Out-Domination Number Of Generalized De Bruijn Digraphs, G. Marimuthu, B. Johnson Dec 2014

Private Out-Domination Number Of Generalized De Bruijn Digraphs, G. Marimuthu, B. Johnson

Applications and Applied Mathematics: An International Journal (AAM)

Dominating sets are widely applied in the design and efficient use of computer networks. They can be used to decide the placement of limited resources, so that every node has access to the resource through neighbouring node. The most efficient solution is one that avoids duplication of access to the resources. This more restricted version of minimum dominating set is called an private dominating set. A vertex v in a digraph D is called a private out-neighbor of the vertex u in S (subset of V(D)) if u is the only element in the intersection of in-neighborhood set of v …

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Difference Cordial Labeling Of Graphs Obtained From Triangular Snakes, R. Ponraj, S. S. Narayanan Dec 2014

Difference Cordial Labeling Of Graphs Obtained From Triangular Snakes, R. Ponraj, S. S. Narayanan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we investigate the difference cordial labeling behavior of corona of triangular snake with the graphs of order one and order two and also corona of alternative triangular snake with the graphs of order one and order two.

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Reichenbach Fuzzy Set Of Transitivity, Samina Ashraf, Muhammad A. Javed Jun 2014

Reichenbach Fuzzy Set Of Transitivity, Samina Ashraf, Muhammad A. Javed

Applications and Applied Mathematics: An International Journal (AAM)

Fuzzy implicators are the basic ingredients of many applications. So it becomes essential to study the various features of an implicator before implementing it in any practical application. This paper discusses the properties of transitivity of a fuzzy relation on a given universe and measure of fuzzy transitivity defined in terms of the Reichenbach fuzzy implicator which is an s-implicator.

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Reducibility Of Eulerian Graphs And Digraphs, Akram B. Attar Dec 2013

Reducibility Of Eulerian Graphs And Digraphs, Akram B. Attar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper the concept of reducibility in graph theory is discussed, and the deletable vertex (edge) in graph (digraph) is defined. The class of graphs (digraphs) ℛ is called vertex (edge) reducible if for any G∈ ℛ either ℛ is the trivial graph (null graph) or it contains a vertex (edge) v such that G-v∈ ℛ. We introduce some classes of graphs (digraphs) which are reducible and others which are not. The vertex reducibility and edge reducibility of Eulerian graphs and Eulerian digraphs have also been studied.

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Generalizations Of Two Statistics On Linear Tilings, Toufik Mansour, Mark Shattuck Dec 2012

Generalizations Of Two Statistics On Linear Tilings, Toufik Mansour, Mark Shattuck

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study generalizations of two well-known statistics on linear square-and-domino tilings by considering only those dominos whose right half covers a multiple of 􀝇, where 􀝇 is a fixed positive integer. Using the method of generating functions, we derive explicit expressions for the joint distribution polynomials of the two statistics with the statistic that records the number of squares in a tiling. In this way, we obtain two families of q -generalizations of the Fibonacci polynomials. When 􀝇 􀵌 1, our formulas reduce to known results concerning previous statistics. Special attention is payed to the case 􀝇 …

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K-Total Product Cordial Labelling Of Graphs, R. Ponraj, M. Sundaram, M. Sivakumar Dec 2012

K-Total Product Cordial Labelling Of Graphs, R. Ponraj, M. Sundaram, M. Sivakumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we introduce the k-Total Product cordial labelling of graphs. Also we investigate the 3-Total Product cordial labelling behaviour of some standard graphs.

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Q -Analogs Of Identities Involving Harmonic Numbers And Binomial Coefficients, Toufik Mansour, Mark Shattuck, Chunwei Song Jun 2012

Q -Analogs Of Identities Involving Harmonic Numbers And Binomial Coefficients, Toufik Mansour, Mark Shattuck, Chunwei Song

Applications and Applied Mathematics: An International Journal (AAM)

Recently, McCarthy presented two algebraic identities involving binomial coefficients and harmonic numbers, one of which generalizes an identity used to prove the Apéry number supercongruence. In 2008, Prodinger provided human proofs of identities initially obtained by Osburn and Schneider using the computer program Sigma. In this paper, we establish q -analogs of a fair number of the identities appearing in McCarthy (Integers 11 (2011): A37) and Prodinger (Integers 8 (2008): A10) by making use of q -partial fractions.

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Pattern Avoiding Partitions, Sequence A054391 And The Kernel Method, Toufik Mansour, Mark Shattuck Dec 2011

Pattern Avoiding Partitions, Sequence A054391 And The Kernel Method, Toufik Mansour, Mark Shattuck

Applications and Applied Mathematics: An International Journal (AAM)

Sequence A054391 in OEIS, which we will denote by an , counts a certain two-pattern avoidance class of the permutations of size n . In this paper, we provide additional combinatorial interpretations for these numbers in terms of finite set partitions. In particular, we identify six classes of the partitions of size n , all of which have cardinality an and each avoiding two classical patterns. We use both algebraic and combinatorial methods to establish our results. In one apparently more difficult case, to show the result, we make use of the kernel method in solving a system …

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Mathematical Modeling, A Small Step In A Right Direction, Reza D. Noubary Jun 2011

Mathematical Modeling, A Small Step In A Right Direction, Reza D. Noubary

Applications and Applied Mathematics: An International Journal (AAM)

Models developed by mathematicians/statisticians based on criterion such as goodness of fit often leads to a “best” model only for the data utilized. Moreover the parameters in such models often do not have physical interpretations and as such their validity cannot be checked by other means. This article makes argument against modeling processes that do not incorporate information from discipline related to the origin of data and presents an example to demonstrate benefits of doing so.

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