Results 21 to 30 of about 107 (98)
Discrete Mathematics & Theoretical Computer Science, 2023 Mixed graphs have both directed and undirected edges. A mixed cage is a regular mixed graph of given girth with minimum possible order. In this paper mixed cages are studied. Upper bounds are obtained by general construction methods and computer searches.
Geoffrey Exoo
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The hull number of an oriented graph
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 36, Page 2265-2275, 2003., 2003 We present characterizations of connected graphs G of order n ≥ 2 for which h+(G) = n. It is shown that for every two integers n and m with 11≤n−≤m≤(n2), there exists a connected graph G of order n and size m such that for each integer k with 2 ≤ k ≤ n, there exists an orientation of G with hull number G.
Gary Chartrand +2 more
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Products Of Digraphs And Their Competition Graphs
Discussiones Mathematicae Graph Theory, 2016 If D = (V, A) is a digraph, its competition graph (with loops) CGl(D) has the vertex set V and {u, v} ⊆ V is an edge of CGl(D) if and only if there is a vertex w ∈ V such that (u, w), (v, w) ∈ A.
Sonntag Martin, Teichert Hanns-Martin
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The second out-neighborhood for local tournaments
Open Mathematics, 2020 Sullivan stated the conjectures: (1) every oriented graph has a vertex x such that d ++(x) ≥ d −(x) and (2) every oriented graph has a vertex x such that d ++(x) + d +(x) ≥ 2d −(x)
Li Ruijuan, Liang Juanjuan
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An algebraic framework of weighted directed graphs
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 58, Page 3657-3678, 2003., 2003 We show that an algebraic formulation of weighted directed graphs leads to introducing a k‐vector space equipped with two coproducts Δ and Δ˜ verifying the so‐called coassociativity breaking equation (Δ˜⊗id)Δ=(id⊗Δ)Δ˜. Such a space is called an L‐coalgebra.
Philippe Leroux
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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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Homomorphically Full Oriented Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 Homomorphically full graphs are those for which every homomorphic image is isomorphic to a subgraph. We extend the definition of homomorphically full to oriented graphs in two different ways.
Thomas Bellitto +2 more
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On incidence algebras and directed graphs
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 5, Page 301-305, 2002., 2002 The incidence algebra I(X, ℝ) of a locally finite poset (X, ≤) has been defined and studied by Spiegel and O′Donnell (1997). A poset (V, ≤) has a directed graph (Gv, ≤) representing it. Conversely, any directed graph G without any cycle, multiple edges, and loops is represented by a partially ordered set VG.
Ancykutty Joseph
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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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Families of (1, 2)‐symplectic metrics on full flag manifolds
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 11, Page 651-664, 2002., 2002 We obtain new families of (1, 2)‐symplectic invariant metrics on the full complex flag manifolds F(n). For n ≥ 5, we characterize n − 3 different n‐dimensional families of (1, 2)‐symplectic invariant metrics on F(n). Each of these families corresponds to a different class of nonintegrable invariant almost complex structures on F(n).
Marlio Paredes
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