Results 11 to 20 of about 1,974,122 (287)

New Bounds for the α-Indices of Graphs

Mathematics, 2020
Let G be a graph, for any real 0≤α≤1, Nikiforov defines the matrix Aα(G) as Aα(G)=αD(G)+(1−α)A(G), where A(G) and D(G) are the adjacency matrix and diagonal matrix of degrees of the vertices of G.
Eber Lenes, Exequiel Mallea-Zepeda, Jonnathan Rodríguez   +2 more
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Independence densities of hypergraphs [PDF]

, 2013
We consider the number of independent sets in hypergraphs, which allows us to define the independence density of countable hypergraphs. Hypergraph independence densities include a broad family of densities over graphs and relational structures, such as ...
Bonato, Anthony, Brown, Jason, Mitsche, Dieter, Pralat, Pawel   +3 more
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On the k-Component Independence Number of a Tree

Discrete Dynamics in Nature and Society, 2021
Let G be a graph and k≥1 be an integer. A subset S of vertices in a graph G is called a k-component independent set of G if each component of GS has order at most k.
Shuting Cheng, Baoyindureng Wu
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On the Independence Number of Cayley Digraphs of Clifford Semigroups

Mathematics, 2023
Let S be a Clifford semigroup and A a subset of S. We write Cay(S,A) for the Cayley digraph of a Clifford semigroup S relative to A. The (weak, path, weak path) independence number of a graph is the maximum cardinality of an (weakly, path, weakly path ...
Krittawit Limkul, Sayan Panma
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The Minimum Spectral Radius of Graphs with the Independence Number [PDF]

, 2013
In this paper, we investigate some properties of the Perron vector of connected graphs. These results are used to characterize that all extremal connected graphs with having the minimum (maximum) spectra radius among all connected graphs of order $n=k ...
Jin, Ya-Lei, Zhang, Xiao-Dong
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Further Results on Packing Related Parameters in Graphs

Discussiones Mathematicae Graph Theory, 2022
Given a graph G = (V, E), a set B ⊆ V (G) is a packing in G if the closed neighborhoods of every pair of distinct vertices in B are pairwise disjoint. The packing number ρ(G) of G is the maximum cardinality of a packing in G. Similarly, open packing sets
Mojdeh Doost Ali, Samadi Babak, Yero Ismael G.   +2 more
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The critical window for the classical Ramsey-Tur\'an problem [PDF]

, 2012
The first application of Szemer\'edi's powerful regularity method was the following celebrated Ramsey-Tur\'an result proved by Szemer\'edi in 1972: any K_4-free graph on N vertices with independence number o(N) has at most (1/8 + o(1)) N^2 edges.
A. Frieze, A. Frieze, A. W. Goodman, B. Bollobás, B. Sudakov, C. Borgs, D. Conlon, D. Conlon, D. Conlon, E. Schmidt, E. Szemerédi, E. Szemerédi, E. Szemerédi, I. Levitt, I. Z. Ruzsa, J. Balogh, J. Balogh, J. Fox, J. Fox, J. Fox, J. Komlós, J. Komlós, Jacob Fox, K. Ball, M. Simonovits, M. Simonovits, N. Alon, P. Châu, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, Po-Shen Loh, R. L. Graham, U. Feige, V. Rödl, V. T. Sós, W. T. Gowers, W. T. Gowers, W. T. Gowers, Yufei Zhao   +42 more
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Coloring Some Finite Sets in ℝn

Discussiones Mathematicae Graph Theory, 2013
This note relates to bounds on the chromatic number χ(ℝn) of the Euclidean space, which is the minimum number of colors needed to color all the points in ℝn so that any two points at the distance 1 receive different colors. In [6] a sequence of graphs Gn
Balogh József, Kostochka Alexandr, Raigorodskii Andrei   +2 more
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On the signed $2$-independence number of graphs

Electronic Journal of Graph Theory and Applications, 2017
In this paper, we study the signed 2-independence number in graphs and give new sharp upper and lower bounds on the signed 2-independence number of a graph by a simple uniform approach.
S.M. Hosseini Moghaddam, D.A. Mojdeh, Babak Samadi, Lutz Volkmann   +3 more
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Connected Domination Number and a New Invariant in Graphs with Independence Number Three [PDF]

Computer Science Journal of Moldova, 2021
Adding a connected dominating set of vertices to a graph $G$ increases its number of Hadwiger $h(G)$. Based on this obvious property in [2] we introduced a new invariant $\eta(G)$ for which $\eta(G)\leq h(G)$. We continue to study its property.
Vladimir Bercov
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