Results 231 to 240 of about 1,156,434 (264)

SEMIGROUPS WITH MAXIMUM COMMUTING REGULARITY DEGREE

JP Journal of Algebra, Number Theory and Applications, 2017
Summary: The commuting regularity degree, \(\mathrm{dcr}(S)\) of a non-group semigroup \(S\) is defined and studied recently by the authors [Creat. Math. Inform. 24, No. 1, 43--47 (2015; Zbl 1349.20044)], where \(\mathrm{dcr}(S)\) is the probability that a pair \((x,y)\) of the elements of \(S\) is a commuting regular pair (the pair \((x,y)\) is called
Firuzkuhy, A., Doostie, H.
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Maximum Degree Condition and Group Connectivity

Graphs and Combinatorics, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Xiaoxia, Li, Xiangwen
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Irredundance and Maximum Degree in Graphs

Combinatorics, Probability and Computing, 1997
It is proved that the smallest cardinality among the maximal irredundant sets in an n–vertex graph with maximum degree Δ([ges ]2) is at least 2n/3Δ. This substantially improves a bound by Bollobás and Cockayne [1]. The class of graphs which attain this bound is characterised.
Cockayne, E. J., Mynhardt, C. M.
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Maximum energy trees with two maximum degree vertices

Journal of Mathematical Chemistry, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Xueliang, Yao, Xiangmei, Zhang, Jianbin, Gutman, Ivan   +3 more
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Maximum degree energy

2021
Summary: In this paper, maximum degree energy of graphs is studied. After giving some preliminary new results, bounds for the maximum degree eigenvalues are obtained for a general graph. Also bounds on the maximum degree eigenvalues of some frequently used graph classes are given by means of combinatorial, number theoretical and analysis methods.
CANGÜL, İSMAİL NACİ, SARAVANAN, K, PRAKASHA, KN, RAO, K. S.   +3 more
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Embedding Arbitrary Graphs of Maximum Degree Two

Journal of the London Mathematical Society, 1993
Let \(\delta (H)\) and \(\Delta (H)\) denote the minimum and maximum degrees of a graph \(H\), respectively. The following result is shown: If \(H\) is a graph of order \(n\) with \(\delta (H) \geq (2n-1)/3\), then any graph \(G\) of order at most \(n\) for which \(\Delta (G) \leq 2\) is a subgraph of \(H\). The \(\delta\)-bound is best possible.
Aigner, Martin, Brandt, S.
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The Maximum Degree of a Random Graph

Combinatorics, Probability and Computing, 2000
Let 0 < p < 1, q = 1 − p and b be fixed and let G ∈ [Gscr ](n, p) be a graph on n vertices where each pair of vertices is joined independently with probability p. We show that the probability that every vertex of G has degree at most pn + b √npq is equal to (c + o(1))n, for c = c(b) the root of a certain equation.
Riordan, Oliver, Selby, Alex
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The Maximum Degree of Random Planar Graphs

Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, 2012
Summary: \textit{C. McDiarmid} and \textit{B. A. Reed} [Comb. Probab. Comput. 17, No. 4, 591--601 (2008; Zbl 1160.05018)] showed that the maximum degree \(\Delta _n\) of a random labeled planar graph with \(n\) vertices satisfies with high probability (w.h.p.) \[ c_1 \log n < \Delta_n
Drmota, M., Giménez, O., Noy, M., Panagiotou, K., Steger, A.   +4 more
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Generalized maximum degree

2001
The generalized maximum degree \(\Delta_k(G)\) of a graph \(G\) of order \(n\geq k\) is the maximum cardinality of the union of the neighbourhoods of \(k\) of its vertices. The authors study bounds on \(\Delta_k(G)\) in terms of the order \(n\), the maximum degree \(\Delta(G)=\Delta_1(G)\) and the total domination number of \(G\).
Haynes, Teresa W., Markus, Lisa R.
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