Ordering Unicyclic Connected Graphs with Girth g ≥ 3 Having Greatest SK Indices

Abstract

For a graph, the SK index is equal to the half of the sum of the degrees of the vertices, the SK1 index is equal to the half of the product of the degrees of the vertices, and the SK2 index is equal to the half of the square of the sum of the degrees of the vertices. This paper shows a simple and unified approach to the greatest SK indices for unicyclic graphs by using some transformations and characterizes these graphs with the first, second, and third SK indices having order r ≥ 5 and girth g ≥ 3, where girth is the length of the shortest cycle in a graph.