In this paper, it is explicitly determined the r-dynamic chromatic number of direct product any given path with either a complete graph or wheel graph. Illustrative examples are shown for each one cases that studied throughout paper.

We show that every connected induced subgraph of a graph G is dominated by an split if and only C-free, where C set six graphs which includes P7 C7, each containing P5. A similar characterization shown for the class are complete graph. Motivated these results, we study structural descriptions some classes (P7, C7)-free graphs. In particular, give C4, gem)-free diamond)-free Using satisfies χ(G)...

The Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph and the Hosoya index of a graph is defined as the total number of the matchings of the graph. In this paper, we give formula for Merrifield-Simmons and Hosoya indices of some classes of cartesian product of two graphs K{_2}×H, where H is a path graph P{_n}, cyclic graph C{_n}, or star gra...

In this paper, we study the complexity of edge monitoring problem. A vertex v monitors an e if both endpoints together with form a triangle in graph. Given graph G=(V,E) and weight function on edges c where c(e) is number that needs e, problem to seek minimum subset S such every monitored by at least vertices S. Therefore, several classes as complete graphs, block cographs, split interval graph...

The isolated toughness of a noncomplete graph G is defined as: , where C(G) the collection all vertex cutsets and i(G − Y) stands for number vertices in Y. If complete graph, we set . This parameter closely related to existence factors fractional graphs. These are well-studied within theory, have various applications several fields computer science. In this article, pay our attention computatio...

In this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. Also, density and balanced irregular vague graphs are discussed and some of their properties are established. Finally we give an application of vague digraphs.

For fixed integers r, l ≥ 0, a graph G is called an (r, l)-graph if the vertex set V (G) can be partitioned into r independent sets and l cliques. This brings us to the following natural parameterized questions: Vertex (r, l)-Partization and Edge (r, l)-Partization. An input to these problems consist of a graph G and a positive integer k and the objective is to decide whether there exists a set...

A graph is said to be well-edge-dominated if all its minimal edge dominating sets are minimum. It known that every G also equimatchable, meaning maximal matching in maximum. In this paper, we show a connected, triangle-free, nonbipartite, graph, then one of three graphs. We characterize the split graphs and Cartesian products. particular, connected product $$G\Box H$$ well-edge-dominated, where...

in this note by considering a complete lattice l, we define thenotion of an l-fuzzy hyperrelation on a given non-empty set x. then wedefine the concepts of (pom)l-fuzzy graph, hypergraph and subhypergroupand obtain some related results. in particular we construct the categories ofthe above mentioned notions, and give a (full and faithful) functor form thecategory of (pom)l-fuzzy subhypergroups ...