The Common Neighborhood Graph and Its Energy

Common Neighborhood Graph

Let G be a simple graph with vertex set {v1, v2, … , vn}. The common neighborhood graph of G, denoted by con(G), is a graph with vertex set {v1, v2, … , vn}, in which two vertices are adjacent if and only if they have at least one common neighbor in the graph G. In this paper, we compute the common neighborhood of some composite graphs. In continue, we investigate the relation between hamiltoni...

On the Common–neighborhood Energy of a Graph

Characteristics of Common Neighborhood Graph under Graph Operations and on Cayley Graphs

Let G(V;E) be a graph. The common neighborhood graph (congraph) of G is a graph with vertex set V , in which two vertices are adjacent if and only if they have a common neighbor in G. In this paper, we obtain characteristics of congraphs under graph operations; Graph :::::union:::::, Graph cartesian product, Graph tensor product, and Graph join, and relations between Cayley graphs and its c...

Some Graph Polynomials of the Power Graph and its Supergraphs

‎In this paper‎, ‎exact formulas for the dependence‎, ‎independence‎, ‎vertex cover and clique polynomials of the power graph and its‎ ‎supergraphs for certain finite groups are presented‎.

Neighborhood total domination of a graph and its complement

A neighborhood total dominating set in a graph G is a dominating set S of G with the property that the subgraph induced by N(S), the open neighborhood of the set S, has no isolated vertex. The neighborhood total domination number γnt(G) is the minimum cardinality of a neighborhood total dominating set of G. Arumugam and Sivagnanam introduced and studied the concept of neighborhood total dominat...

supply and demand security of energy in central asia and the caucasus

امنیت انرژی به معنی عرضه مداوم و پایدار همراه با قیمت های معقول در حامل های انرژی، که تهدیدات امنیتی، سیاسی، اقتصادی، محیط زیستی و روانی را کاهش دهد. امروزه نفت و گاز تنها، کالای تجاری نیست بلکه بعنوان ابزار سیاسی مورد استفاده قرار می گیرد.اختلاف میان روسیه و اکراین بر سر انرژی در ژانویه 2006، تهدیدی برای امنیت انرژی اروپا ایجاد کرد. در این تحقیق ما تلاش کردیم که نقش انرژی آسیای میانه و قفقاز ر...