THE g-NON-COMMUTING GRAPH FOR SOME FINITE GROUPS AND THEIR RANDIC INDEX.
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| Title: | THE g-NON-COMMUTING GRAPH FOR SOME FINITE GROUPS AND THEIR RANDIC INDEX. |
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| Authors: | Roslly, Siti Rosllydia Dania1, Alimon, Nur Idayu2, Mohammad, Siti Afiqah3, Sarmin, Nor Haniza4 |
| Source: | Advances & Applications in Discrete Mathematics. Apr2026, Vol. 43 Issue 3, p299-320. 22p. |
| Subjects: | Finite groups, Molecular graphs |
| Abstract: | A molecular graph is an essentially non-numerical mathematical object, and to link molecular topology with molecular properties, its information is converted into a numerical characteristic called a topological index (TOI). The study on TOIs has grown significantly since 1947 and many types of topological indices have been developed until recently. The g-non-commuting graph is an extension of the noncommuting graph. For a finite group G and a fixed element, G ∈ g the g-non-commuting graph is defined with the vertex set G, where two distinct vertices x and y are adjacent if [x,y] ≠ g, and [x,y] ≠ g-1. Meanwhile, the Randić index, a degree-based TOI, is defined as the sum of the reciprocal square roots of the product of the degrees of two adjacent vertices in a graph. In this study, the general form of the g-non-commuting graph associated to the dihedral, the generalized quaternion, and the quasidihedral groups, are introduced. Then, based on these graphs, their Randić indices are determined and some examples are also presented to illustrate the main theorems. These results can be beneficial to predict the physicochemical properties of the molecules. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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