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Ars Mathematica Contemporanea, 2012 A graph G is singular if the zero-one adjacency matrix has the eigenvalue zero. The multiplicity of the eigenvalue zero is called the nullity of G . For two vertices y and z of G , we call ( G , y , z ) a device with respect to y and z .
Irene Sciriha +4 more
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On Minimum Wiener Polarity Index of Unicyclic Graphs with Prescribed Maximum Degree
Journal of Applied Mathematics, 2014 The Wiener polarity index of a connected graph G is defined as the number of its pairs of vertices that are at distance three. By introducing some graph transformations, in different way with that of Huang et al., 2013, we determine the minimum Wiener ...
Jianping Ou, Xing Feng, Saihua Liu
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On Acyclic Structures with Greatest First Gourava Invariant
Journal of Chemistry, 2022 Let ξ be a simple connected graph. The first Gourava index of graph ξ is defined as GO1ξ=∑μη∈Eξdμ+dη+dμdη, where dμ indicates the degree of vertex μ.
Mariam Imtiaz +4 more
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AKCE International Journal of Graphs and Combinatorics, 2023 For a connected simple graph G, the inverse degree index and forgotten index are defined as [Formula: see text] and [Formula: see text] respectively, where [Formula: see text] denotes the degree of vertex u in G.
Mohammad Ali Manian +2 more
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An advance in infinite graph models for the analysis of transportation networks
International Journal of Applied Mathematics and Computer Science, 2016 This paper extends to infinite graphs the most general extremal issues, which are problems of determining the maximum number of edges of a graph not containing a given subgraph.
Cera Martín, Fedriani Eugenio M.
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Extremal graphs of multiplicative sum Zagreb index [PDF]
Notes on Number Theory and Discrete MathematicsThe multiplicative sum Zagreb index, regarded as the multiplicative version of the first Zagreb index, is defined as the product of the degree sum over all pairs of adjacent vertices.
Chunlei Xu +3 more
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Maximal tree and unicylic graph for Euler Sombor index with given diameter
AKCE International Journal of Graphs and CombinatoricsThe study of topological descriptors is essential for understanding the underlying structures of graphs and networks. Numerous numerical descriptors associated with graphs have been used to analyze their overall structure.
Zahid Raza +3 more
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P_{m}-saturated graphs with minimum size [PDF]
Opuscula Mathematica, 2004 By \(P_m\) we denote a path of order \(m\). A graph \(G\) is said to be \(P_m\)-saturated if \(G\) has no subgraph isomorphic to \(P_m\) and adding any new edge to \(G\) creates a \(P_m\) in \(G\). In 1986 L. Kászonyi and Zs.
Aneta Dudek, A. Paweł Wojda
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Maximum Reciprocal Degree Resistance Distance Index of Unicyclic Graphs
Discrete Dynamics in Nature and Society, 2020 The reciprocal degree resistance distance index of a connected graph G is defined as RDRG=∑u,v⊆VGdGu+dGv/rGu,v, where rGu,v is the resistance distance between vertices u and v in G. Let Un denote the set of unicyclic graphs with n vertices.
Gai-Xiang Cai, Xing-Xing Li, Gui-Dong Yu
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Some Bond Incident Degree Indices of (Molecular) Graphs with Fixed Order and Number of Cut Vertices
Discrete Dynamics in Nature and Society, 2021 A bond incident degree (BID) index of a graph G is defined as ∑uv∈EGfdGu,dGv, where dGw denotes the degree of a vertex w of G, EG is the edge set of G, and f is a real-valued symmetric function. The choice fdGu,dGv=adGu+adGv in the aforementioned formula
Abeer M. Albalahi +3 more
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