Alpha labeling of splitting graph of a gutman tree

Abstract

The splitting graph S'(G) of graph G results by introducing a new point a' with respect to each point a of G such that N(a) equals to N(a') where N(a) and N(a') are the neighborhood sets of a and a' respectively. The Gutman tree is also known as benzenoid tree and caterpillar tree. In this paper, it is proved that a splitting graph of a Gutman tree satisfies an alpha labeling.