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| Some Bounds for the Steiner-Harary Index of a Graph |
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| KeyWord:Harary index, Steiner index, Steiner-Harary index |
| Author Name | Affiliation | | B. Sarveshkumar | Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore -560 056, India | | B. Chaluvaraju | Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore -560 056, India | | M. C. Mahesh Kumar | Department of Mathematics, GFGC, K. R. Puram, Bangalore -560 036, India |
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| Abstract: |
| The Steiner distance for the set $S\subseteq V(G)$ would simply be the number of edges in the minimal subtree connecting them and is denoted as $d_G(S)$. The Steiner-Harary index is $SH_k(G)$, defined as the sum of the reciprocal of the Steiner distance for all subsets with $k$ vertices in $G$. In this article, we calculate the exact value of $SH_k(G)$ for specific graphs and establish new best possible lower and upper bounds and characterization. Furthermore, we explore the relationship between $SH_k(G)$ and other graph indices based on Steiner distance. |
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