A result on the consecutive adjacent degree of a semigraph

Abstract

Semigraphs introduced by E.Sampathkumar [3] is a new type of generalization of the concept of graph. A semigraph G (V, X ) on the nonempty set of vertices V and the set of edges X consists of n tuples (u1, u2,..., un) of distinct elements belonging to the set V for various n 2, with the following conditions: (i) Any n tuple (u1, u2,..., un) = (u1, u2,..., u1) and (ii) Any two such tuples have at most one element in common. For a vertex v in a semigraph G, we can define various types of degrees. This paper presents a new result on the sum of consecutive adjacent degree in semigraphs.