TY - JOUR
T1 - Some Bounds for the Steiner-Harary Index of a Graph
AU - Sarveshkumar , B.
AU - Chaluvaraju , B.
AU - Kumar , M. C. Mahesh
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 1446
EP - 1460
PY - 2025
DA - 2025/07
SN - 7
DO - http://doi.org/10.12150/jnma.2025.1446
UR - https://global-sci.org/intro/article_detail/jnma/24245.html
KW - Harary index, Steiner index, Steiner-Harary index.
AB - <p style="text-align: justify;">The Steiner distance for the set $S ⊆ V (G)$ 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.</p>