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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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Rational exponents in extremal graph theory [PDF]
, 2016 Given a family of graphs H, the extremal number ex(n,H) is the largest m for which there exists a graph with n vertices and m edges containing no graph from the family H as a subgraph.
David Conlon +6 more
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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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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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A Note on the Maximum Genus of Graphs with Diameter 4 [PDF]
, 2007 Let G be a simple graph with diameter four, if G does not contain complete subgraph K3 of order ...
WeiLi, He, Xiang, Ren, Lin, Zhao
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Proofs by Transformation in Extremal Graph Theory [PDF]
, 2022 A graph is a mathematical model representing binary relationships between elements of a set. It is composed of two sets: the set of the elements called the vertices and a set of pairs of vertices called the edges.
Devillez, Gauvain
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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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