The Minimum Sombor Index for Unicyclic Graphs with Fixed Diameter

Abstract

As a novel member of the class of vertex-degree-based topological indices, the so-called Sombor index was recently introduced by Gutman on the chemical graphs. In this paper, we present the minimum Sombor index for unicyclic graphs with the diameter D>_2.

On the Maximum Sombor Index of Unicyclic Graphs with a Fixed Girth

“…Te graphs possessing the least and largest values of the SO index among all unicyclic graphs with a fxed order were found independently in [10,11]. Liu [12] (respectively, Alidadi et al [13]) reported the graphs attained the highest value (respectively, least value) of the SO index among all unicyclic graphs with a fxed diameter and order. Te graphs attaining the minimum (respectively, maximum) SO index over the class of all unicyclic graphs with a fxed maximum degree (respectively, matching number) and order were characterized in [14] (respectively, in [15]).…”

Relations between Energy and Sombor Index

“…where d x is the degree of vertex x. Some results for the mentioned indices can be found in [1], [3], [6], [7], [10], [12], [13], [14] and the references therein.…”

On the Firefighter problem of full icosahedral symmetry fullerene graphs

“…The icosahedral fullerene graphs, introduced by Andova and Škrekovski in 2013 [1], are the graphs such that the centers of the pentagonal faces form an icosahedron. The full icosahedral symmetry fullerene graphs G i,0 , where i ≥ 1, is a perfectly symmetric icosahedral fullerene graph such that each pentagonal face equidist exactly i units to other 5 pentagonal faces.…”