Pyramidal Sum Labeling In Graphs

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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 … 𝑝𝑞 such that the induced edge labels obtained by the Sum of the labels of the end vertices are the first q pyramidal numbers where 𝑝𝑞 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 Pn⨀K 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

EP ID EP393938
DOI 10.9790/9622-0804011519.
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