Generalization of Randic Index of the Non-commuting Graph for Some Finite Groups

• Published in: MALAYSIAN JOURNAL OF FUNDAMENTAL AND APPLIED SCIENCES
• Main Authors: Roslly, Siti Rosllydia Dania; Ab Halem, Nur Fatimah Az Zahra; Zailani, Nur Syasya Sahira; Alimon, Nur Idayu; Mohammad, Siti Afiqah
• Format: Article
• Language: English
• Published: PENERBIT UTM PRESS 2023
• Subjects: Science & Technology - Other Topics
• Online Access: https://www-webofscience-com.uitm.idm.oclc.org/wos/woscc/full-record/WOS:001141998400014
• ISSN: 2289-5981; 2289-599X
• DOI: 10.11113/mjfas.v19n5.3047

Randic index is one of the classical graph-based molecular structure descriptors in the field of mathematical chemistry. The Randic index of a graph is calculated by summing the reciprocals of the square root of the product of the degrees of two adjacent vertices in the graph. Meanwhile, the non-commuting graph is the graph of vertex set whose vertices are non-central elements and two distinct vertices are joined by an edge if and only if they do not commute. In this paper, the general formula of the Randic index of the non-commuting graph associated to three types of finite groups are presented. The groups involved are the dihedral groups, the generalized quaternion groups, and the quasi- dihedral groups. Some examples of the Randic index of the non-commuting graph related to a certain order of these groups are also given based on the main results.