• SEQUENTIAL PYRAMIDAL GRAPHS

Abstract

Let G = (V, E) be a graph with p vertices and q edges. A Graph G is said to admit Sequential  Pyramidal labeling if its vertices can be labeled from the set of integers  such that the induced edge labels obtained by the integral part of the division of the labels of the end vertices such that the numerators are greater than the denominators are the sequence of natural numbers from   in which the sum of the squares of the edge labels is the q^th Pyramidal number. A Graph G which admits such a labeling is called a Sequential Pyramidal Graph. In this Paper we prove that all Cycles, Caterpillars, the graph  and all Jahangir graphs are Sequential Pyramidal graphs and also introduce some classes of Non-Sequential Pyramidal graphs. By a graph we mean a finite, undirected graph without multiple edges or loops. For graph theoretic terminology, we refer to Bondy and Murty [2] and Harary [4]. For number theoretic terminology, we refer to M. Apostal [1] and for graph labeling we refer to J.A. Gallian [3].