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.

‎in this paper we introduce mixed unitary cayley graph $m_{n}$‎ ‎$(n>1)$ and compute its eigenvalues‎. ‎we also compute the energy of‎ ‎$m_{n}$ for some $n$‎.

In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...

Let G be a graph and t : V ( G ) , {0, 1}, where t(V(G)) is even. (If X~_ V(G), then t ( X ) : = E { t (x):xeX}. ) A t-join is a set F ~ E ( G ) with d~(x)=t(x) (mod 2), Vx e V(G). (dF(x) denotes the number of edges of F incident with x, where loops count twice.) t-joins contain Chinese postman tours, matchings and minimum weight paths as a special case. (el. [1, 7]). If X c V(G), let 6 ( X ) =...