On the Spectral Radius and Sombor Energy of the Non-Commuting Graph for Dihedral Groups
Mamika Ujianita Romdhini,
Athirah Nawawi
Abstract:The non-commuting graph, denoted by , is defined on a finite group , with its vertices are elements of excluding those in the center of . In this graph, two distinct vertices are adjacent whenever they do not commute in . The graph can be associated with several matrices including the most basic matrix, which is the adjacency matrix, , and a matrix called Sombor matrix, denoted by . The entries of are either the square root of the sum of the squares of degrees of two distinct adjacent vertices, or zero othe… Show more
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