Total influence number in complementary prisms

Abstract

The graph labeling problem that appears in graph theory has a fast development recently. Numerous variations of labeling have been investigated in the literature. The total influence number is a new approach to the concept of graph labeling. The total influence number can be viewed as vertex labeling problems concerned with the sum of the labels. Although many vertex labeling problems concerning with the sum of all of the labels study to minimize the sum, the total influence number has the aim of maximizing the sum. This means that this parameter attempt to maximize the profit associated with each vertex. In this paper, we consider the total influence number in complementary prisms. We determined the total influence number of GG for specific graphs G.