General Randić Index of Unicyclic Graphs With Given Number of Pendant Vertices

Abstract

© 2022 the authors. This is an open access article under the CC BY (International 4.0) license (www.creativecommons.org/licenses/by/4.0/). Abstract For a ∈ R and a graph G, the general Randić index is defined as Ra(G) = ∑ uv∈E(G)[dG(u)dG(v)] , where E(G) is the edge set of G, and dG(u) and dG(v) are degrees of the vertices u and v in G, respectively. For −0.64 ≤ a < 0, we give lower bounds on the general Randić index for unicyclic graphs with given number of pendant vertices, and with given order and number of pendant vertices. The extremal graphs are presented as well. Lower bounds on the classical Randić index are corollaries of our bounds on the general Randić index.