Further Results on Vertex Equitable Graphs

Let G be a graph with p vertices and q edges and . A graph G is said to be vertex equitable 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, |vf(a)−vf(b)|≤1 and the induced edge labels are 1,2,3,…,q where vf(a) is the number of vertices v with f(v)=a for a∈A. The vertex labeling f is known as vertex equitable labeling. In this paper, we prove that NQ(m), DA(Qm)⊙nK1, DA(Tm)⊙nK1, the graph obtained by subdividing the edges of the path Pn in Pn⊙K1 and Pn⊙2K1 are vertex equitable graphs.