Results 41 to 50 of about 1,022,735 (236)
The Largest Component in Critical Random Intersection Graphs
Discussiones Mathematicae Graph Theory, 2018 In this paper, through the coupling and martingale method, we prove the order of the largest component in some critical random intersection graphs is n23$n^{{2 \over 3}}$ with high probability and the width of scaling window around the critical ...
Wang Bin, Wang Longmin, Xiang Kainan
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Connected Domination Critical Graphs with Cut Vertices
Discussiones Mathematicae Graph Theory, 2020 A graph G is said to be k- γc-critical if the connected domination number of G, γc(G), is k and γc(G + uv) < k for any pair of non-adjacent vertices u and v of G. Let G be a k-γc-critical graph and ζ (G) the number of cut vertices of G. It was proved, in
Kaemawichanurat Pawaton +1 more
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, 2015 The study of entrywise powers of matrices was originated by Loewner in the pursuit of the Bieberbach conjecture. Since the work of FitzGerald and Horn (1977), it is known that $A^{\circ \alpha} := (a_{ij}^\alpha)$ is positive semidefinite for every ...
Guillot, Dominique +2 more
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Graphs and CombinatoricsAbstract In 1971, Graham and Pollak provided a formula for the determinant of the distance matrix of any tree on n vertices. Yan and Yeh reproved this by exploiting the fact that pendant vertices can be deleted from trees without changing the remaining entries of the distance matrix.
Joshua Cooper, Gabrielle Tauscheck
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Chinese Science Bulletin, 1997 Summary: Let \(G\) be a graph and let \(a\), \(b\) be nonegative integers with \(a\leq b\). Then graph \(G\) is called an \((a, b, k)\)-critical graph if after deleting any \(k\) vertices of \(G\) the remaining graph of \(G\) has an \([a, b]\)-factor. In this paper a necessary and sufficient condition for a graph to be \((a, b, k)\)-critical is given ...
Liu, G. Z., Wang, J. F.
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Total $k$-distance domination critical graphs [PDF]
Transactions on Combinatorics, 2016 A set $S$ of vertices in a graph $G=(V,E)$ is called a total$k$-distance dominating set if every vertex in $V$ is withindistance $k$ of a vertex in $S$.
Doost Ali Mojdeh +3 more
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Structures of Critical Nontree Graphs with Cutwidth Four
Mathematics, 2023 The cutwidth of a graph G is the smallest integer k (k≥1) such that the vertices of G are arranged in a linear layout [v1,v2,...,vn], in such a way that for each i=1,2,...,n−1, there are at most k edges with one endpoint in {v1,v2,...,vi} and the other ...
Zhenkun Zhang, Hongjian Lai
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3-Factor-criticality in domination critical graphs
Discrete Mathematics, 2007 For an integer \(k\geq 2\) a graph \(G\) is \(k\)-\(\gamma\)-critical if the domination number \(\gamma(G)\) of \(G\) is \(k\) and \(\gamma(G+e) = k-1\) for every edge \(e \not\in E(G)\). For an integer \(t \geq 1\) a graph \(G\) is \(t\)-factor-critical if \(G-S\) has a perfect matching for every set \(S\) of \(t\) vertices of \(G\).
Ananchuen, Nawarat, Plummer, Michael D.
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Domination criticality in product graphs
AKCE International Journal of Graphs and Combinatorics, 2015 A connected dominating set is an important notion and has many applications in routing and management of networks. Graph products have turned out to be a good model of interconnection networks. This motivated us to study the Cartesian product of graphs G
M.R. Chithra, A. Vijayakumar
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Isolated toughness and fractional (a,b,n)-critical graphs
Connection Science, 2023 A graph G is a fractional $ (a,b,n) $ -critical graph if removing any n vertices from G, the resulting subgraph still admits a fractional $ [a,b] $ -factor.
Wei Gao, Weifan Wang, Yaojun Chen
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