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. 2024 Sep 30;10(19):e38578.
doi: 10.1016/j.heliyon.2024.e38578. eCollection 2024 Oct 15.

Sombor characteristic values of cographs

Zahid Raza  1 , Bilal Ahmad Rather  1   2 , Muhammad Imran  3
Affiliations

Sombor characteristic values of cographs

Zahid Raza et al. Heliyon. .

Abstract

A unique class of cograph is examined, that is defined recursively as C = C ( n 1 ) = K ‾ n 1 , and C = C ( n 1 , n 2 , … , n i ) = C ( n 1 , n 2 , … , n i - 1 ) ∪ K n i ‾ , for 2 ≤ i ≤ k . The Sombor spectrum of C is calculated, the Sombor spectral radius and establish the sharp bounds for the Sombor index, and the greatest and smallest Sombor characteristic values. We present results on the Sombor energy of cographs and identify the graphs that reach the inequalities. Also, we characterize cographs with simple Sombor characteristic values and cographs with unique characteristic values.

Keywords: 05C12; 05C50; 15A18; Characteristic values; Cographs graphs; Sombor index; Sombor matrix.

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Conflict of interest statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Figures

Figure 1
Figure 1
Cograph C(3,2,2,3).
See this image and copyright information in PMC

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