We consider only finite undirected graphs without loops or multiple edges. Let G be a graph with vertex set V(G) and edge set E(G). For a vertex x ∈V(G), we write NG(v) for the set of vertices of V(G) adjacent to v, NG[v] for NG(v) ⋃{v}, and dG(v) = |NG(v)| for the degree of v in G. If S and T are disjoint subsets of V(G), then eG(S,T) denotes the number of edges that join S and T , and G− S de...

In this paper, we investigate the concept of resolving dominating set in a graph. particular, characterize sets join, corona and lexicographic product two graphs determine domination number these graphs.

An edge labeling of a connected graph $G = (V, E)$ is said to be local antimagic if it bijection $f:E \to\{1,\ldots ,|E|\}$ such that for any pair adjacent vertices $x$ and $y$, $f^+(x)\not= f^+(y)$, where the induced vertex label $f^+(x)= \sum f(e)$, with $e$ ranging over all edges incident $x$. The chromatic number $G$, denoted by $\chi_{la}(G)$, minimum distinct labels labelings $G$. In this...

Motivated by the Eulerian ribbon graph minors, in this paper we introduce notion of checkerboard colourable minors for graphs and its dual: bipartite graphs. abstract graphs, another i.e. join are also introduced. Using these then give excluded minor characterizations classes plane

In this paper, using matrix techniques, we compute the Ihara-zeta function and number of spanning trees join two semi-regular bipartite graphs. Furthermore, show that spectrum graphs can determine each other.