Pyramidal Sum Labeling In Graphs
Journal Title: International Journal of engineering Research and Applications - Year 2018, Vol 8, Issue 4
Abstract
Let G = (V, E) be a graph with p vertices and q edges. A graph G is said to admit Pyramidal Sum labeling if its vertices can be labeled by nonnegative integers 0,1,2 ⊠ðð such that the induced edge labels obtained by the Sum of the labels of the end vertices are the first q pyramidal numbers where ðð is the qth pyramidal number. A graph G which admits a Pyramidal Sum labeling is called a Pyramidal Sum graph. In this Paper we prove that the one vertex union of t copies of any Path, the graphs got by attaching the roots of different Stars to one vertex, Comb graph PnâšK and all Lobsters are Pyramidal Sum Graphs and show that some graphs are Unpyramidal. By a graph we mean a finite, undirected graph without multiple edges or loops. For graph theoretic terminology, we refer to Harary [4] and Bondy and Murty [2]. For number theoretic terminology, we refer to M. Apostal [1] and Niven and Herbert S. Zuckerman [5].
Authors and Affiliations
H. Velwet Getzimah, D. S. T. Ramesh
Keywords
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