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Information Inequalities via Submodularity and a Problem in Extremal Graph Theory [PDF]
Entropy, 2022 The present paper offers, in its first part, a unified approach for the derivation of families of inequalities for set functions which satisfy sub/supermodularity properties.
Igal Sason
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It Is Better to Be Semi-Regular When You Have a Low Degree [PDF]
EntropyWe study the algebraic connectivity for several classes of random semi-regular graphs. For large random semi-regular bipartite graphs, we explicitly compute both their algebraic connectivity as well as the full spectrum distribution. For an integer d∈3,7,
Theodore Kolokolnikov
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On tricyclic graphs with maximum atom–bond sum–connectivity index [PDF]
HeliyonThe sum-connectivity, Randić, and atom-bond connectivity indices have a prominent place among those topological indices that depend on the graph's vertex degrees.
Sadia Noureen +5 more
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Exponential second Zagreb index of chemical trees [PDF]
Transactions on Combinatorics, 2021 Cruz, Monsalve and Rada [Extremal values of vertex-degree-based topological indices of chemical trees, Appl. Math. Comput. 380 (2020) 125281] posed an open problem to find the maximum value of the exponential second Zagreb index for chemical ...
Selvaraj Balachandran, Tomas Vetrik
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On some interconnections between combinatorial optimization and extremal graph theory [PDF]
Yugoslav Journal of Operations Research, 2004 The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set.
Cvetković Dragoš M. +2 more
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Note on the temperature Sombor index
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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Reducing the maximum degree of a graph: comparisons of bounds
Theory and Applications of Graphs, 2021 Let $\lambda(G)$ be the smallest number of vertices that can be removed from a non-empty graph $G$ so that the resulting graph has a smaller maximum degree.
Peter Borg
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On the Boundary of Incidence Energy and Its Extremum Structure of Tricycle Graphs
Frontiers in Physics, 2020 With the wide application of graph theory in circuit layout, signal flow chart and power system, more and more attention has been paid to the network topology analysis method of graph theory.
Hongyan Lu, Zhongxun Zhu
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A note on the Ramsey numbers for theta graphs versus the wheel of order 5
AKCE International Journal of Graphs and Combinatorics, 2018 The study of exact values and bounds on the Ramsey numbers of graphs forms an important family of problems in the extremal graph theory. For a set of graphs S and a graph F , the Ramsey number R (S , F) is the smallest positive integer r such that for ...
Mohammed M.M. Jaradat +3 more
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Triangles in Ks-saturated graphs with minimum degree t
Theory and Applications of Graphs, 2020 For $n \geq 15$, we prove that the minimum number of triangles in an $n$-vertex $K_4$-saturated graph with minimum degree 4 is exactly $2n-4$, and that there is a unique extremal graph.
Craig Timmons +3 more
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