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| Abstract : Universiti Pendidikan Sultan Idris |
| The Randi? index R(G) of a graph G is the sum of the weights (dudv)? 2 of all edges uv in G, where du denotes the degree of vertex u. Du and Zhou [On Randi? indices of trees, unicyclic graphs, and bicyclic graphs, Int. J. Quantum Chem. 111 (2011), 27602770] determined the n-vertex unicyclic graphs with the third maximum for n ? 5, the fourth maximum for n ? 7 and the fifth maximum for n ? 8. Recently, Li et al. [The Randi? indices of trees, unicyclic graphs and bicyclic graphs, Ars Comb. 127 (2016), 409419] obtained the n-vertex unicyclic graphs with the sixth maximum and the seventh maximum for n ? 9 and the eighth maximum for n ? 10. In this paper, we characterize the n-vertex unicyclic graphs with the ninth maximum, the tenth maximum, the eleventh maximum, the twelfth maximum and the thirteenth maximum of Randi? values. 2023 Azarbaijan Shahid Madani University. |
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