Characterization of Spider Graphs with Pair Sum Modulo Labeling

Abstract

Labeling a graph involves assigning numbers to its vertices, edges, or both, depending on certain requirements. Numerous applications have made use of graph labeling. A mapping  for a simple graph G˓(V,E) is referred to as a pair sum modulo (PSM) labeling if [f(u)+f(v)](mod |V|) is distinct for each edge uv. A PSM graph is a graph that allows PSM labelling. This article demonstrates there exists PSM labelling of spider graph with k legs of varying lengths (1,2,.,6).