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THE GUTMAN INDEX OF UNICYCLIC GRAPHS
Discrete Mathematics, Algorithms and Applications, 2012Let G be a connected graph with vertex set V(G). The Gutman index of G is defined as S(G) = ∑{u, v}⊆V(G) d(u)d(v)d(u, v), where d(u) is the degree of vertex u, and d(u, v) denotes the distance between u and v. In this paper, we characterize n-vertex unicyclic graphs with girth k, having minimal Gutman index.
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Axioms
With geometric significance, the Euler Sombor index of a graph Γ is defined as EP(Γ)=∑{uv}∈E(Γ)d(u)2+d(v)2+d(u)d(v). It originates from the mathematical distance property and has been proven to have good chemical applications in octane isomers.
Zhenhua Su, Zikai Tang
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With geometric significance, the Euler Sombor index of a graph Γ is defined as EP(Γ)=∑{uv}∈E(Γ)d(u)2+d(v)2+d(u)d(v). It originates from the mathematical distance property and has been proven to have good chemical applications in octane isomers.
Zhenhua Su, Zikai Tang
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On the atom-bond sum-connectivity spectral radius of unicyclic graphs
Discrete Mathematics LettersLet G be a graph with n vertices. For i = 1 , 2 , . . . , n , let d i be the degree of vertex v i in G . The atom-bond sum-connectivity (ABS) matrix of G is an n × n matrix whose ( i, j ) -entry is equal to (cid:112) ( d i + d j − 2) / ( d i + d j ) if ...
Zhen Lin, Yingke Liu
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Roman domination in unicyclic graphs
Journal of Discrete Mathematical Sciences and Cryptography, 2012Abstract A Roman dominating function on a graph G = (V, E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f (v) = 2. The weight of a Roman dominating function is the value w (f) = ∑ u∈V f(u).
P. Roushini Leely Pushpam +1 more
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On $${A_{\alpha }}$$ A α -spectrum of a unicyclic graph
Journal of combinatorial optimization, 2022Hua He +3 more
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Bond incident degree indices of fixed-order unicyclic graphs
Discrete Mathematics LettersA connected graph with the same order and size is known as a unicyclic graph. For a vertex u in a graph, we denote its degree by d u . For a unicyclic graph G of a given order, we investigate an extremal problem concerning the degree-based graph ...
Akbar Ali, K. C. Das, Adel A. Attiya
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EXTREMAL IRREGULARITY OF TOTALLY SEGREGATED UNICYCLIC GRAPHS
Far East Journal of Mathematical Sciences (FJMS), 2019Summary: The irregularity of a simple graph \(G=(V,E)\) is defined as \(irr(G)=\sum_{uv\in E(G)}|\mathrm{deg}_G(v)|\), where \(\mathrm{deg}_G(u)\) denotes the degree of a vertex \(u\in V(G)\). A graph in which any two adjacent vertices have distinct degrees is a totally segregated graph. In this paper we determine maximum and minimum of \(\{irr(G): \ G
Jorry, T. F., Parvathy, K. S.
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Symmetry
The topological index (TI), sometimes referred to as the connectivity index, is a molecular descriptor calculated based on the molecular graph of a chemical compound.
Muhammad Yasin Khan +2 more
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The topological index (TI), sometimes referred to as the connectivity index, is a molecular descriptor calculated based on the molecular graph of a chemical compound.
Muhammad Yasin Khan +2 more
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On the Kirchhoff index of a unicyclic graph and the matchings of the subdivision
Discrete Applied Mathematics, 2021Yulan Chen, Weigen Yan
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Extremal Unicyclic Graphs for the Euler Sombor Index
Match-communications in Mathematical and in Computer ChemistryThe Euler Sombor index of a graph G is a recently introduced topological index, defined ...
Alexandru-Petre Tache +2 more
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