For a given hypergraph, an orientation can be assigned to the vertex-edge incidences. This orientation is used to define the adjacency and Laplacian matrices. Continuing the study of these matrices associated to an oriented hypergraph, several related structures are investigated including: the incidence dual, the intersection graph (line graph), and the 2-section. The intersection graph is show...

An incidence in a graph G is a pair (v, e) with v ∈ V (G) and e ∈ E(G), such that v and e are incident. Two incidences (v, e) and (w, f) are adjacent if v = w, or e = f , or the edge vw equals e or f . The incidence chromatic number of G is the smallest k for which there exists a mapping from the set of incidences of G to a set of k colors that assigns distinct colors to adjacent incidences. In...

Neutrosopic sets were introduced by Smarandache [2] which are the generalization of fuzzy sets and intuitionistic fuzzy sets. The Neutrosophic sets have many applications in medical, management sciences, life sciences and engineering, graph theory, robotics, automata theory and computer science. The single valued neutrosophic graphs were introduced by Broumi, Talea, Bakali and Smarandache [5]. ...

We give a fairly elementary and simple proof that shows that the number of incidences between m points and n lines in R, so that no plane contains more than s lines, is O (

The shortest path problem (SPP) is one of the most important combinatorial optimization problems in graph theory due to its various applications. The uncertainty existing in the real world problems makes it difficult to determine the arc lengths exactly. The fuzzy set is one of the popular tools to represent and handle uncertainty in information due to incompleteness or inexactness. In most cas...

Introduced implicitly by Brualdi and Massey [3] in their work on the strong chromatic index of multigraphs, the arc incidence graph AI(G) of a graph G is defined as the square of the line graph of the incidence graph of G. We describe a linear-time algorithm for recognizing arc incidence graphs and reconstructing a graph with no isolated vertices from its arc incidence graph.

Ravindra Bapat We consider two-person zero-sum games, or matrix games, in which the pure strategies of the players are the vertices, or the edges of a graph, and the payoff is determined by the incidence structure. We identify some cases where the value and the optimal strategies can be explicitly determined. In particular, we consider the incidence matrix game in which the payoff matrix is the...

Let G be a simple graph with vertex set V (G) = {v1, v2, . . . , vn} and edge set E(G) = {e1, e2, . . . , em}. Similar to the Randić matrix, here we introduce the Randić incidence matrix of a graph G, denoted by IR(G), which is defined as the n × m matrix whose (i, j)-entry is (di) 1 2 if vi is incident to ej and 0 otherwise. Naturally, the Randić incidence energy IRE of G is the sum of the sin...

Abstract: In this paper we analyzed the spreading rate of virus between incoming and outgoing links to a website. We have taken the website http://www.pantechsolutions.net/. This website is modeled as an intuitionistic fuzzy graph G = (V,E, μ, γ) by considering the navigation of the customers. In this intuitionistic fuzzy graph, the links are considered as vertices and the path of the links is ...

We prove that the incidence chromatic number of every 3-degenerated graph G is at most ∆(G)+ 4. It is known that the incidence chromatic number of every graph G with maximum average degree mad(G) < 3 is at most ∆(G)+3. We show that when ∆(G) ≥ 5, this bound may be decreased to ∆(G) + 2. Moreover, we show that for every graph G with mad(G) < 22/9 (resp. with mad(G) < 16/7 and ∆(G) ≥ 4), this bou...