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Discrete Mathematics Letters, 2021 A Special Volume on Chemical Graph Theory in Memory of Nenad TrinajsticWe introduce a degree–based variable topological index inspired on the power (or generalized) mean. We name this new index as the mean Sombor index: SOα(G) = P uv∈E(G) [(d α u + d α v
J. A. Mendez-Bermudez +3 more
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Sombor index of directed graphs [PDF]
Heliyon, 2022 Let D be a digraph with set of arcs A. The Sombor index of D is defined asSO(D)=12∑uv∈A(du+)2+(dv−)2,where du+ and dv− are the out-degree and in-degree of the vertices u and v of D.
Roberto Cruz, Juan Monsalve, Juan Rada
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Symmetry, 2021 The concept of Sombor index (SO) was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological index and is denoted by Sombor index SO: SO=SO(G)=∑vivj∈E(G)dG(vi)2+dG(vj)2√, where dG(vi) is the degree of vertex vi
Cangul, Ismail +3 more
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Sombor spectra of chain graphs [PDF]
Heliyon, 2023 We study the Sombor index and the Sombor spectral properties of chain graphs. In particular, an explicit formula for the Sombor index is given, the Sombor eigenvalues are discussed, bounds on the largest and the smallest Sombor eigenvalues are presented,
Muhammad Imran, Bilal Ahmad Rather
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Comparative study of Sombor index and its various versions using regression models for top priority polycyclic aromatic hydrocarbons [PDF]
Scientific ReportsThe aromatic compounds having structural configurations with two or more fused benzene rings are the polycyclic aromatic hydrocarbons (PAHs). Topological indices are valuable tools for studying the structure property relationships of PAHs and also helps ...
B. Kirana, M. C. Shanmukha, A. Usha
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Multiplicative Sombor index of graphs [PDF]
Discrete Mathematics Letters, 2022 Summary: The Sombor index of a graph \(G\) is defined as \(SO(G) =\sum_{uv \in E(G)}\sqrt{d^2_G(u) +d^2_G(v)}\), where \(d_G(u)\) denotes the degree of the vertex \(u\) of \(G\). Accordingly, the multiplicative Sombor index of \(G\) can be defined as \(\prod_{SO}(G) =\prod_{uv \in E(G)} \sqrt{d^2_G(u) +d^2_G(v)}\).
Hechao Liu
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Eccentric sombor index of graphs and its role in the structure-property relationship analysis of polycyclic aromatic compounds [PDF]
Scientific ReportsThis article focuses on the eccentric Sombor index, a variant of the degree-based Sombor index in which vertex degrees are replaced by their eccentricities.
Balkishbanu Khaji +2 more
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Sombor topological indices for different nanostructures [PDF]
Heliyon, 2023 Euclidean geometry is utilized to establish the Sombor graph parameter and its invariants. It is sum of all adjacent vertices in graph theory dϒ2+dΓ2 where dϒ is the degree of the vertex ϒ.
Muhammad Imran +4 more
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, 2021 We present the bounds in terms of other important graph parameters for general Sombor index which generalises both the forgotten index and the Sombor index. We also explore the Nordhaus-Gaddum-type result for the general Sombor index.
Mawiong, Sainkupar Mn +1 more
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Note on the temperature Sombor index [PDF]
Vojnotehnički Glasnik, 2023 Introduction/purpose: The temperature of a vertex of a graph of the order n is defined as d/(n-d), where d is the vertex degree. The temperature variant of the Sombor index is investigated and several of its properties established. Methods: Combinatorial
Ivan Gutman
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