Results 191 to 200 of about 16,499 (231)
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Regular Digraphs Containing a Given Digraph
Canadian Mathematical Bulletin, 1984AbstractLet the maximum degree d of a digraph D be the maximum of the set of all outdegrees and indegrees of the points of D. We prove that every digraph D of order P and maximum degree d has a d-regular superdigraph H with at most d + 1 more points, and that this bound, which is independent of p, is best possible.
Harary, Frank, Karabed, Razmik
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CKI-Digraphs, Generalized Sums and Partitions of Digraphs
Graphs and Combinatorics, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hortensia Galeana-Sánchez, Mika Olsen
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SIAM Journal on Discrete Mathematics, 2010
One of the classical results in packing theory states that every graph of order $n$ and size less than or equal to $n-2$ is packable in its complement. Moreover, the bound is sharp because the star is not packable. A similar problem arises for digraphs, namely, to find the maximal number $f_D(n)$ such that every digraph of order $n$ and size less than ...
Agnieszka Görlich, Andrzej Zak
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One of the classical results in packing theory states that every graph of order $n$ and size less than or equal to $n-2$ is packable in its complement. Moreover, the bound is sharp because the star is not packable. A similar problem arises for digraphs, namely, to find the maximal number $f_D(n)$ such that every digraph of order $n$ and size less than ...
Agnieszka Görlich, Andrzej Zak
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Converse Lyapunov Theorems for Discrete-Time Switching Systems With Given Switches Digraphs
IEEE Transactions on Automatic Control, 2019It is proved in this paper that the existence of suitable multiple Lyapunov functions is a necessary and sufficient condition for a discrete-time nonlinear switching system, with given switches digraph, to be globally asymptotically stable.
P. Pepe
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Canadian Mathematical Bulletin, 1966
The line - graph of an ordinary graph G is that graph whose points can be put in one-to-one correspondence with the lines of G in such a way that two points of are adjacent if and only if the corresponding lines of G are adjacent. This concept originated with Whitney [ 5 ], has the property that its (point) chromatic number equals the line chromatic
Chartrand, G., Stewart, M. J.
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The line - graph of an ordinary graph G is that graph whose points can be put in one-to-one correspondence with the lines of G in such a way that two points of are adjacent if and only if the corresponding lines of G are adjacent. This concept originated with Whitney [ 5 ], has the property that its (point) chromatic number equals the line chromatic
Chartrand, G., Stewart, M. J.
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On super‐edge‐connected digraphs and bipartite digraphs
Journal of Graph Theory, 1992AbstractA maximally edge‐connected digraph is called super‐λ if every minimum edge disconnecting set is trivial, i.e., it consists of the edges adjacent to or from a given vertex. In this paper sufficient conditions for a digraph to be super‐λ are presented in terms of parameters such as diameter and minimum degree.
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Domination in rough fuzzy digraphs with application
Soft Computing - A Fusion of Foundations, Methodologies and Applications, 2023Uzma Ahmad, Tahira Batool
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Journal of Graph Theory, 1980
AbstractA hypotraceable digraph is a digraph D = (V, E) which is not traceable, i.e., does not contain a (directed)Hamiltonian path, but for which D ‐ v is traceable for all ve ∈ V. We prove that a hypotraceable digraph of order n exists iff n ≥ 7 and that for each k ≥ 3 there are infinitely many hypotraceable oriented graphs with a source and a sink ...
Martin Grötschel +2 more
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AbstractA hypotraceable digraph is a digraph D = (V, E) which is not traceable, i.e., does not contain a (directed)Hamiltonian path, but for which D ‐ v is traceable for all ve ∈ V. We prove that a hypotraceable digraph of order n exists iff n ≥ 7 and that for each k ≥ 3 there are infinitely many hypotraceable oriented graphs with a source and a sink ...
Martin Grötschel +2 more
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Planar Digraphs of Digirth Four are 2-Colorable
SIAM Journal on Discrete Mathematics, 2016Neumann-Lara conjectured in 1985 that every planar digraph with digirth at least three is 2-colourable, meaning that the vertices can be 2-coloured without creating any monochromatic directed cycles.
Zhentao Li, B. Mohar
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