| Summary: | For a graph, the <i>SK</i> index is equal to the half of the sum of the degrees of the vertices, the <i>SK</i><sub>1</sub> index is equal to the half of the product of the degrees of the vertices, and the <i>SK</i><sub>2</sub> 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 <i>SK</i> indices for unicyclic graphs by using some transformations and characterizes these graphs with the first, second, and third <i>SK</i> indices having order <i>r</i> ≥ 5 and girth <i>g</i> ≥ 3, where girth is the length of the shortest cycle in a graph.
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