Results 21 to 30 of about 1,376 (263)
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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On the spread of outerplanar graphs
Special Matrices, 2022 The spread of a graph is the difference between the largest and most negative eigenvalue of its adjacency matrix. We show that for sufficiently large nn, the nn-vertex outerplanar graph with maximum spread is a vertex joined to a linear forest with Ω(n ...
Gotshall Daniel +2 more
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Extremal optimization for graph partitioning [PDF]
Physical Review E, 2001 34 pages, RevTex4, 1 table and 20 ps-figures included, related papers available at http://www.physics.emory.edu/faculty/boettcher/
Stefan Boettcher, Allon G. Percus
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Discrete Mathematics, 1999 The \(\alpha\)-weight of an edge \(xy\) of a graph \(G\) is \(d(x)^\alpha\cdot d(y)^\alpha\) where \(d(x)\) and \(d(y)\) are the degrees of the vertices \(x\) and \(y\). The \(\alpha\)-weight of \(G\) is the sum of the \(\alpha\)-weights of its edges. The authors establish the \(\alpha\)-weight of a graph with any fixed number of edges for \(\alpha=1\)
Béla Bollobás +2 more
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Asymptotic Structure for the Clique Density Theorem
Discrete Analysis, 2020 Asymptotic structure for the clique density theorem, Discrete Analysis 2020:19, 26 pp. Turán's theorem, which is regarded as the "first" result in extremal graph theory, is the statement that the $K_r$-free graph on $n$ vertices with the largest number ...
Jaehoon Kim +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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Maximum Reciprocal Degree Resistance Distance Index of Bicyclic Graphs
Discrete Dynamics in Nature and Society, 2021 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 ℬn denote the set of bicyclic graphs without common edges and with n
Gaixiang Cai, Xing-Xing Li, Guidong Yu
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Extremal Graph Realizations and Graph Laplacian Eigenvalues
SIAM Journal on Discrete Mathematics, 2023 For a regular polyhedron (or polygon) centered at the origin, the coordinates of the vertices are eigenvectors of the graph Laplacian for the skeleton of that polyhedron (or polygon) associated with the first (non-trivial) eigenvalue. In this paper, we generalize this relationship.
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An Extremal Property of Turán Graphs [PDF]
The Electronic Journal of Combinatorics, 2010 Let ${\cal F}_{n,t_r(n)}$ denote the family of all graphs on $n$ vertices and $t_r(n)$ edges, where $t_r(n)$ is the number of edges in the Turán's graph $T_r(n)$ – the complete $r$-partite graph on $n$ vertices with partition sizes as equal as possible.
Felix Lazebnik, Spencer Tofts
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Extremal graphs for edge blow-up of graphs [PDF]
Journal of Combinatorial Theory, Series B, 2022 Given a graph $H$ and an integer $p$, the {\it edge blow-up} of $H$, denoted as $H^{p+1}$, is the graph obtained from replacing each edge in $H$ by a clique of size $p+1$ where the new vertices of the cliques are all different. The Turán numbers for edge blow-up of matchings were first studied by Erdős and Moon.
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