Common Neighborhood Energy of Commuting Graphs of Finite Groups

Nath, Rajat Kanti, Fasfous, Walaa Nabil Taha, Das, Kinkar Chandra and Shang, Yilun (2021) Common Neighborhood Energy of Commuting Graphs of Finite Groups. Symmetry, 13 (9). p. 1651. ISSN 2073-8994

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The commuting graph of a finite non-abelian group G with center Z(G), denoted by Γc(G), is a simple undirected graph whose vertex set is G∖Z(G), and two distinct vertices x and y are adjacent if and only if xy=yx. Alwardi et al. (Bulletin, 2011, 36, 49-59) defined the common neighborhood matrix CN(G) and the common neighborhood energy Ecn(G) of a simple graph G. A graph G is called CN-hyperenergetic if Ecn(G)>Ecn(Kn), where n=|V(G)| and Kn denotes the complete graph on n vertices. Two graphs G and H with equal number of vertices are called CN-equienergetic if Ecn(G)=Ecn(H). In this paper we compute the common neighborhood energy of Γc(G) for several classes of finite non-abelian groups, including the class of groups such that the central quotient is isomorphic to group of symmetries of a regular polygon, and conclude that these graphs are not CN-hyperenergetic. We shall also obtain some pairs of finite non-abelian groups such that their commuting graphs are CN-equienergetic.

Item Type: Article
Additional Information: Funding information: This research was funded by National Research Foundation fund from the Korean government, Grant No. 2021R1F1A1050, and UoA Flexible Fund from Northumbria University, Grant No. 201920A1001
Uncontrolled Keywords: commuting graph; CN-energy; finite group
Subjects: G100 Mathematics
G400 Computer Science
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: Elena Carlaw
Date Deposited: 08 Sep 2021 08:35
Last Modified: 08 Sep 2021 08:45

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