CONNECTED EDGE AND ENTIRE DOMINATION OF INVOLUTORY ADDITION CAYLEY GRAPH

Abstract

Graph theory is one of the most advanced branches of discrete mathematics with a variety of applications to different branches of Science and Technology. For a positive integer n > 1, the involutory addition Cayley graph G⁺(Zn, Iv) is the graph whose vertex set is Zn = {0, 1, 2, 3, ..., n − 1} and edge set E(Gn) = {xy / x, y ∈ Zn, x + y ∈ Iv}, where Iv = {x ∈ Zn : x² ≡ 1 (mod n)} is the set of involutory elements of Zn. By taking involutory addition Cayley graphs G⁺(Zn, Iv), the authors evaluated graph-related connected edge domination numbers and entire domination numbers. In this paper, connected edge domination number and entire domination number of the involutory addition Cayley graphs G⁺(Zn, Iv) were discussed.