On the Non-Commuting Graph of the Group $U_{6n}$
Sanhan Khasraw, C.H. Jaf, Nor Haniza Sarmin, Ibrahim Gambo

TL;DR
This paper investigates the properties of the non-commuting graph of the group U_{6n}, including its structural parameters and polynomial invariants, providing new formulas and insights into its combinatorial characteristics.
Contribution
It introduces explicit formulas for the resolving polynomial and other graph invariants of the non-commuting graph of U_{6n}, expanding understanding of its combinatorial structure.
Findings
Derived the general formula for the resolving polynomial.
Calculated the independent number, clique number, and chromatic number.
Determined the detour index, eccentric connectivity, and total eccentricity.
Abstract
A non-commuting graph of a finite group is a graph whose vertices are non-central elements of and two vertices are adjacent if they don't commute in . In this paper, we study the non-commuting graph of the group and explore some of its properties including the independent number, clique and chromatic numbers. Also, the general formula of the resolving polynomial of the non-commuting graph of the group are provided. Furthermore, we find the detour index, eccentric connectivity, total eccentricity and independent polynomials of the graph.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Graph theory and applications · Advanced Graph Theory Research
