Independence and domination number of order two element graph over a group
Soumen Pradhan, Sukhendu Kar, Bijon Biswas · Discrete Mathematics Algorithms and Applications · 2024
Let [Formula: see text] be a group. Then the order two element graph of [Formula: see text] is the simple undirected graph whose vertex set consists of all elements of [Formula: see text] and two distinct vertices [Formula: see text] are adjacent if and only if either [Formula: see text], where [Formula: see text] is the identity element of [Formula: see text]. This graph is denoted by [Formula: see text]. In this paper, we first establish some beautiful results on Merrifield–Simmons index of order two element graph over a group. After that we characterize the product of two order two element graph over two groups. Moreover we study some important results on domination number of order two element graph over a group.