Results 31 to 40 of about 834 (84)
About (k, l)-Kernels, Semikernels and Grundy Functions in Partial Line Digraphs
Discussiones Mathematicae Graph Theory, 2019 Let D be a digraph of minimum in-degree at least 1. We prove that for any two natural numbers k, l such that 1 ≤ l ≤ k, the number of (k, l)-kernels of D is less than or equal to the number of (k, l)-kernels of any partial line digraph ℒD. Moreover, if l
Balbuena C. +2 more
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Incidence matrices and line graphs of mixed graphs
Special Matrices, 2023 In the theory of line graphs of undirected graphs, there exists an important theorem linking the incidence matrix of the root graph to the adjacency matrix of its line graph. For directed or mixed graphs, however, there exists no analogous result.
Abudayah Mohammad +2 more
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How to construct the symmetric cycle of length 5 using Haj\'os construction with an adapted Rank Genetic Algorithm [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 In 2020 Bang-Jensen et. al. generalized the Haj\'os join of two graphs to the class of digraphs and generalized several results for vertex colorings in digraphs.
Juan Carlos García-Altamirano +2 more
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Algorithmic aspects of bipartite graphs
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 2, Page 299-304, 1995., 1995 We generalize previous work done by Donald J. Rose and Robert E. Tarjan [2], who developed efficient algorithms for use on directed graphs. This paper considers an edge elimination process on bipartite graphs, presenting several theorems which lead to an algorithm for computing the minimal fill‐in of a given ordered graph.
Mihály Bakonyi, Erik M. Varness
wiley +1 more source
Total Roman domination on the digraphs
Open Mathematics, 2023 Let D=(V,A)D=\left(V,A) be a simple digraph with vertex set VV, arc set AA, and no isolated vertex. A total Roman dominating function (TRDF) of DD is a function h:V→{0,1,2}h:V\to \left\{0,1,2\right\}, which satisfies that each vertex x∈Vx\in V with h(x ...
Zhang Xinhong, Song Xin, Li Ruijuan
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Existence and uniqueness of solutions to the norm minimum problem on digraphs
Open Mathematics, 2022 In this article, based on the path homology theory of digraphs, which has been initiated and studied by Grigor’yan, Lin, Muranov, and Yau, we prove the existence and uniqueness of solutions to the problem ∥w∥=minu∈Ω2(G),u≠012∥∂u−w∥22+∣u∣1\parallel w ...
Wang Chong
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Unordered Love in infinite directed graphs
International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 4, Page 753-756, 1992., 1992 A digraph D = (V, A) has the Unordered Love Property (ULP) if any two different vertices have a unique common outneighbor. If both (V, A) and (V, A−1) have the ULP, we say that D has the SDULP. A love‐master in D is a vertex ν0 connected both ways to every other vertex, such that D − ν0 is a disjoint union of directed cycles.
Peter D. Johnson Jr.
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Game-Perfect Semiorientations of Forests
Discussiones Mathematicae Graph Theory, 2022 We consider digraph colouring games where two players, Alice and Bob, alternately colour vertices of a given digraph D with a colour from a given colour set in a feasible way. The game ends when such move is not possible any more.
Andres Stephan Dominique +2 more
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Notes on sufficient conditions for a graph to be Hamiltonian
International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 4, Page 825-827, 1991., 1990 The first part of this paper deals with an extension of Dirac′s Theorem to directed graphs. It is related to a result often referred to as the Ghouila‐Houri Theorem. Here we show that the requirement of being strongly connected in the hypothesis of the Ghouila‐Houri Theorem is redundant. The Second part of the paper shows that a condition on the number
Michael Joseph Paul +2 more
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On the digraph of a unitary matrix
, 2003 Given a matrix M of size n, a digraph D on n vertices is said to be the digraph of M, when M_{ij} is different from 0 if and only if (v_{i},v_{j}) is an arc of D.
Grössing Gerhard +5 more
core +2 more sources