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Open access
Aug 2026
Euler Hyperbolic Sombor Index
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
Open access
Aug 2026
Bounds for the Hyperbolic Sombor Index in Terms of the Variable Euler–Sombor Index and Relations to Other Degree-Based Invariants
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...
Wei-Peng Zhang, Saihua Liu, Rui Song
· Mathematics · 0 citations
Open access
Aug 2026
Degree-Ratio Sombor Index
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...
Akbar Ali, Ivan Gutman, Gasper George Nyauli et al.
· Match-communications in Math... · 0 citations
Open access
Oct 2026
Triplet Sombor Index of Graphs
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
Open access
Aug 2026
On the Degree-Ratio Sombor Index: Corrections and New Bounds
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
Open access
Aug 2026
WIENER TYPE TOPOLOGICAL INDICES OF SOME WELL-KNOWN UNICYCLIC GRAPHS
Wiener-type distance-based topological indices (Wiener, Wiener polarity, hyper-Wiener, Harary, reciprocal complementary Wiener, and terminal Wiener) are discussed and recalculated by considering the odd and even cases of n.
H. Topcu, Eda Güner
· Eskişehir Teknik Üniversites... · 0 citations