Results 21 to 30 of about 605,731 (305)
On Extremal Graphs With No Long Paths [PDF]
The Electronic Journal of Combinatorics, 1996 Connected graphs with minimum degree $\delta$ and at least $2\delta + 1$ vertices have paths with at least $2\delta + 1$ vertices. We provide a characterization of all such graphs which have no longer paths.
Asad Ali Ali, William Staton
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On the Roman Edge Domination Number of a Graph [PDF]
, 2010 Let G be a simple graph with vertex set V (G) and edge set E(G)
K. Ebadi +5 more
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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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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 extremal sets without coprimes [PDF]
, 1994 Ahlswede R, Khachatrian LH. On extremal sets without coprimes. Acta Arithmetica.
Levon Khachatrian +4 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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Uniqueness of near-horizon geometries of rotating extremal AdS(4) black holes [PDF]
, 2009 We consider stationary extremal black hole solutions of the Einstein-Maxwell equations with a negative cosmological constant in four dimensions. We determine all non-static axisymmetric near-horizon geometries and all static near-horizon geometries for ...
Lucietti, James, Kunduri, Hari K.
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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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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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