EVEN VERTEX EQUITABLE even LABELING for CORONA and Tp-TREE RELATED GRAPHS

Abstract

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, • • • , 7} if q is even. A graph G is said to be an even vertex equitable even labeling if there exists a vertex labeling/: V(G) A that induces an edge labeling f defined by f(uv) =/(ti)-f f(v) for all edges uv such that for all a and 6 in A, |v/(a)-vy(fc)| < 1 and the induced edge labels are 2,4, • • , 2q, where v/(a) be the number of vertices v with f(v) = a for a 6 A. A graph that admits even vertex equitable even labeling is called an even vertex equitable even graph. In this paper, we prove that Ln O rnK 1, Cn O and Tp-tree related graphs are an even vertex equitable even graph. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.