Aug 2026· Match-communications in Mathematical and in Computer Chemistry· Vol 97, pp. 639· 0 citations
Abstract
The degree-ratio Sombor (DRSO) index is a recently introduced variant of the extensively studied Sombor index. In this paper, we establish an upper bound on the DRSO index in terms of the size, minimum degree, and maximum degree of a graph, which provides the unique graph maximizing the DRSO index among all fixed-order trees. Also, we give an upper bound for the DRSO index in terms of the order, size, and maximum degree of a graph, from which it follows that the star graph uniquely maximizes the DRSO index over the class of all fixed-order connected graphs. In addition, we rectify two results from [MATCH Commun. Math. Comput. Chem. 97 (2027) 135–164], one related to a lower bound on the DRSO index and the other concerning extremal values of the DRSO index among all fixed-order connected graphs. We characterize the graphs that maximize the DRSO index among all fixed-order (i) unicyclic graphs, (ii) trees with a prescribed number of pendent vertices, and (iii) trees with a fixed matching number. Furthermore, we determine the structure of graphs that minimize the DRSO index among all fixed-order k-cyclic graphs, for k ≥ 1 and sufficiently large values of the order.
The degree-ratio Sombor index (DRSO) is a recently introduced geometric degree-based topological invariant. First, we correct an erroneous lower bound involving the Sombor index and rectify the characterization of extremal graphs from the original work on this index [11]. Subsequently, we investigate the relationship b...
Zhou-Jian Shao, A. Jahanbani· Match-communications in Math...· 0 citations
The Hyperbolic Sombor index HSO(G) of a graph G=(V(G),E(G)) is proposed as a new vertex-degree-based topological index. In this paper, we investigate the mathematical properties of this novel vertex-degree-based topological index for general graphs. We first establish tight upper and lower bounds on HSO(G) in terms of...
In this paper, we introduce the Triplet Sombor Index (TSO), a
new degree–based topological index defined over connected triples
of vertices. We also establish several basic properties and bounds
of the index in terms of graph parameters. In particular, we determine extremal trees with respect to TSO, and we prove that...
Mina Abdulkareem Sultan, F. Shaveisi, B. Edalatzadeh· Match-communications in Math...· 0 citations
This work investigates the extremal structural properties of uniform hypertrees with respect to the Sombor index and the Sombor spectral radius, two degree-based measures that capture nonlinear connectivity patterns.
Shashwath S. Shetty, K. Bhat· Match-communications in Math...· 0 citations
Szeged-type bond additive indices are a class of distance-based topological indices defined by counting the vertices or edges that are closer to the end vertices of an edge. Important members of this family include the Szeged index, Mostar index, PI index, SPI index, and the Szeged–Sombor index, together with their cor...
L. Alex, Muhammad Imran· Match-communications in Math...· 0 citations
In this paper, we introduce the Euler hyperbolic Sombor index and investigate its fundamental properties across various classes of graphs. We first establish general lower and upper bounds for this index and examine its relationships with several well-known topological indices, including the Euler Sombor index, the geo...
Esra Öztürk Sözen, Elif Eryaşar, Ivan Gutman et al.· Match-communications in Math...· 0 citations
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