All graph in this paper are members of family of graph tree. Let G is a connected graph, for an ordered set W={w1,w2,...,wk} of vertices and a vertex which is not element of W, then W is dominating set of graph G when the ...

Let G = (V, E) be a graph. A proper k-coloring of graph G is r-dynamic coloring if for every v, the neighbors of vertex v receive at least min { r, d(v) } different colors. The minimum k such that graph G has r-dynamic ...

All graph in this paper is connected and simple graph. Let d(u, v) be a distance between any vertex u and v in graph G = (V, E ). A function : ( ) l V G {1, 2, , } k →  is called vertex irregular k-labelling ...

All graph in this paper is connected and simple graph. Let graph d(u,v) be a distance between any vertex u and v in graph ( ). A functio ( ) * +n is called vertex irregular k-labelling and ( ) where ...

All graph in this paper is connected graph. Let du,v be a distance between any vertex u and v in graph GV,E. A function c :VG 1, 2, , k is called a packing k  coloring if every two vertex of color i are ...

All graph in this paper are connected and simple. Let G = (V, E) be a simple graph, where V (G) is vertex set and E(G) is edge set. The local irregularity vertex coloring of G is l : V (G) → {1, 2, · · · , k} and w : V (G) ...

An elegant labeling on the graph G with n vertex and m edge is a one-to-one mapping (injection function) of the vertex set V (G) to the set of non negative integers {0, 1, 2, 3, . . . , m} such that each edge gets the ...