EVEN VERTEX EQUITABLE EVEN LABELING FOR CORONA AND T-p-TREE RELATED GRAPHS

摘要

Let G be a graph with p vertices and q edges and A = {0, 2, 4, ..., q + 1} if q is odd or A = {0, 2,4, ..., q} if q is even. A graph G is said to be an even vertex equitable even labeling if there exists a vertex labeling f : V(G) -> A that induces an edge labeling f* defined by f* (uv) = f (u) + f (v) for all edges uv such that for all a and b in A, vertical bar v(f)(a) - v(f)(b)vertical bar <= 1 and the induced edge labels are 2, 4, ..., 2q, where v(f)(a) be the number of vertices v with f (v) = a for a is an element of A. A graph that admits even vertex equitable even labeling is called an even vertex equitable even graph. In this paper, we prove that L-n circle dot mK(1), C-n circle dot K-1 and T-p-tree related graphs are an even vertex equitable even graph.