Simply Sequentially Additive Labeling of Some Special Trees
K. Manimekalai, Bharathi Women, Jayapal Baskar Babujee · 2012
A graph labeling is an assignment of integers to the vertices or edges or both subject to certain conditions. Labeled graphs are becoming an increasingly useful family of Mathematical Models from a broad range of applications. Bange, Barkauskas, and slater [1] defined a k-sequentially additive labeling f of a graph G(V,E) as a bijection from V ∪ E to {k, k+1, …, k+|V ∪ E|−1} such that for each edge xy∈E, f(xy) = f(x) + f(y). If k =1, then G(V, E) is said to be 1-sequentially additive graph or a simply sequentially additive graph or briefly, an SSA-graph. They conjectured that all trees are 1-sequentially additive. In this paper we prove the existence of 1- sequentially additive labeling of Bm,n, and its related graph, U n