Chartrand et. al. have introduced γ-labelings of graphs, wherein they studied structural properties of graphs by taking absolute difference of vertex vales. This motivated us to investigate structural properties of graphs when we take sum of vertex values of an edge. Thus we defined edge sum labelings of graphs. Let G=(V,E) be a given graph with p vertices and q edges. An edge sum labeling of a graph G is an injective function f: V(G)→ {0,1,2,…,P-1 that induces a labeling f+: E(G)→ {1,2,…,2p-3} of the edges of G defined by f+(uv)=f(u)+f(v), for each edge e=uv of G. Then the value of an edge sum labeling of G is the sum of the edge values of G. In this paper, I study edge sum labelings of caterpillar, n-ary tree, palm tree and triangular snake.
Volume 11 | 08-Special Issue
Pages: 2097-2100