Resumen de Odd vertex equitable even labeling of graphs

P. Jeyanthi, A. Maheswari, M. Vijayalakshmi

• In this paper, we introduce a new labeling called odd vertex equitable even labeling. Let G be a graph with p vertices and q edges and A = {1, 3,..., q} if q is odd or A = {1, 3,..., q + 1} if q is even. A graph G is said to admit an odd 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 thatfor all a and b in A, |vf (a) —vf (b)| ≤ 1 and the induced edge labels are 2, 4,..., 2q where vf (a) be the number of vertices v with f (v) = a for a ∈ A. A graph that admits odd vertex equitable even labeling is called odd vertex equitable even graph. We investigate the odd vertex equitable even behavior of some standard graphs.