Naslov
On the Sombor index of graphs

Autori
Réti, Tamas ; Došlić, Tomislav ; Ali, Akbar

Izvornik
Contributions to Mathematics (2709-3646) 3 (2021); 11-18

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
chemical graph theory ; topological index ; Sombor index ; bounds ; cyclic graphs.

Sažetak
This paper is concerned with a recently introduced graph invariant, namely the Sombor index. Some bounds on the Sombor index are derived, and then utilized to establish additional bounds by making use of the existing results. One of the direct consequences of one of the obtained bounds is that the cycle graph C n attains the minimum Sombor index among all connected unicyclic graphs of a fixed order n ≥ 4. Graphs having the maximum Sombor index are also characterized from the classes of all connected unicyclic, bicyclic, tricyclic, tetracyclic, and pentacyclic graphs of a fixed order, and a conjecture concerning the maximum Sombor index of graphs of higher cyclicity is stated. A structural result is derived for graphs with integer values of Sombor index. Several possible directions for future work are also indicated.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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