Physical Sciences and Mathematics Commons^™

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.

Structure Of A Total Independent Set, Lewis Stanton

Rose-Hulman Undergraduate Mathematics Journal

Let $G$ be a simple, connected and finite graph with order $n$. Denote the independence number, edge independence number and total independence number by $\alpha(G), \alpha'(G)$ and $\alpha''(G)$ respectively. This paper establishes an upper bound for $\alpha''(G)$ in terms of $\alpha(G)$, $\alpha'(G)$ and $n$. We also describe the possible structures for a total independent set containing a given number of elements.

Between Graphical Zonotope And Graph-Associahedron, Marko Pesovic, Tanja Stojadinovic

Turkish Journal of Mathematics

This manuscript introduces a finite collection of generalized permutohedra associated to a simple graph. The first polytope of this collection is the graphical zonotope of the graph, and the last is the graph-associahedron associated to it. We describe the weighted integer points enumerators for polytopes in this collection as Hopf algebra morphisms of combinatorial Hopf algebras of decorated graphs. In the last section, we study some properties related to $\mathcal{H}$-polytopes.

Supra-Approximation Spaces Using Combined Edges Systems, Hussein R. Jaffer, Khalid Sh. Al’Dzhabri

Al-Qadisiyah Journal of Pure Science

The primary in this paper's notion, the i-space using incident edges system (resp. n-space using non-incidental edges system), is what this study is responsible for generating and investigating. Additionally, we used c-interior to define the c-lower approximations in generalized rough set theory (resp. i-interior and n-interior) Additionally, the c-upper approximations are defined using c-closure (as opposed to i-closure and n-closure), and some of its characteristics are studied.

Mining The Soma Cube For Gems: Isomorphic Subgraphs Reveal Equivalence Classes, Edward Vogel, My Tram

Journal of Humanistic Mathematics

Soma cubes are an example of a dissection puzzle, where an object is broken down into pieces, which must then be reassembled to form either the original shape or some new design. In this paper, we present some interesting discoveries regarding the Soma Cube. Equivalence classes form aesthetically pleasing shapes in the solution set of the puzzle. These gems are identified by subgraph isomorphisms using SNAP!/Edgy, a simple block-based computer programming language. Our preliminary findings offer several opportunities for researchers from middle school to undergraduate to utilize graphs, group theory, topology, and computer science to discover connections between computation and …

Exponents Of Jacobians Of Graphs And Regular Matroids, Hahn Lheem, Deyuan Li, Carl Joshua Quines, Jessica Zhang

Rose-Hulman Undergraduate Mathematics Journal

Let G be a finite undirected multigraph with no self-loops. The Jacobian Jac (G) is a finite abelian group associated with G whose cardinality is equal to the number of spanning trees of G. There are only a finite number of biconnected graphs G such that the exponent of Jac (G) equals 2 or 3. The definition of a Jacobian can also be extended to regular matroids as a generalization of graphs. We prove that there are finitely many connected regular matroids M such that Jac (M) has exponent 2 and characterize all such matroids.

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,..., …

Consecutive Prime And Highly Total Prime Labeling In Graphs, Robert Scholle

Rose-Hulman Undergraduate Mathematics Journal

This paper examines the graph-theoretical concepts of consecutive prime labeling and highly total prime labeling. These are variations on prime labeling, introduced by Tout, Dabboucy, and Howalla in 1982. Consecutive prime labeling is defined here for the first time. Consecutive prime labeling requires that the labels of vertices in a graph be relatively prime to the labels of all adjacent vertices as well as all incident edges. We show that all paths, cycles, stars, and complete graphs have a consecutive prime labeling and conjecture that all simple connected graphs have a consecutive prime labeling.

This paper also expands on work …

Jones Polynomial For Graphs Of Twist Knots, Abdulgani Şahin, Bünyamin Şahin

Applications and Applied Mathematics: An International Journal (AAM)

We frequently encounter knots in the flow of our daily life. Either we knot a tie or we tie a knot on our shoes. We can even see a fisherman knotting the rope of his boat. Of course, the knot as a mathematical model is not that simple. These are the reflections of knots embedded in threedimensional space in our daily lives. In fact, the studies on knots are meant to create a complete classification of them. This has been achieved for a large number of knots today. But we cannot say that it has been terminated yet. There are …

Finite Simple Graphs And Their Associated Graph Lattices, James B. Hart, Brian Frazier

Theory and Applications of Graphs

In his 2005 dissertation, Antoine Vella explored combinatorical aspects of finite graphs utilizing a topological space whose open sets are intimately tied to the structure of the graph. In this paper, we go a step further and examine some aspects of the open set lattices induced by these topological spaces. In particular, we will characterize all lattices that constitute the opens for finite simple graphs endowed with this topology, explore the structure of these lattices, and show that these lattices contain information necessary to reconstruct the graph and its complement in several ways.

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.

On A Generalization Of Kelly's Combinatorial Lemma, Aymen Ben Amira, Jamel Dammak, Hamza Si Kaddour

Turkish Journal of Mathematics

Kelly's combinatorial lemma is a basic tool in the study of Ulam's reconstruction conjecture. A generalization in terms of a family of t -elements subsets of a v -element set was given by Pouzet. We consider a version of this generalization modulo a prime p. We give illustrations to graphs and tournaments.

Some Graph Type Hypersurfaces In A Semi-Euclidean Space, Ikawa Toshihiko, Honda Kyoko

Turkish Journal of Mathematics

We consider some graph type hypersurfaces in a semi-Euclidean space $\Bbb R^{n+1}_{q}$ and give conditions of the dimension $n+1$ and the index $q$ when a hypersurface is lightlike, totally geodesic and minimal.