Results 61 to 70 of about 128 (115)
On kernels by rainbow paths in arc-coloured digraphs
Open Mathematics, 2021 In 2018, Bai, Fujita and Zhang [Discrete Math. 341 (2018), no. 6, 1523–1533] introduced the concept of a kernel by rainbow paths (for short, RP-kernel) of an arc-coloured digraph DD, which is a subset SS of vertices of DD such that (aa) there exists no ...
Li Ruijuan, Cao Yanqin, Zhang Xinhong
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The (1, 2)-step competition graph of a hypertournament
Open Mathematics, 2021 In 2011, Factor and Merz [Discrete Appl. Math. 159 (2011), 100–103] defined the (1,2)\left(1,2)-step competition graph of a digraph. Given a digraph D=(V,A)D=\left(V,A), the (1,2)\left(1,2)-step competition graph of D, denoted C1,2(D){C}_{1,2}\left(D ...
Li Ruijuan, An Xiaoting, Zhang Xinhong
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On some relationships between Leavitt path algebras and Brauer configuration algebras
Open MathematicsWe compare Cuntz–Krieger and Brauer relations inside the same path algebra when every configuration vertex has valency two. Choosing one arrow from each successor pair produces a directed graph, and the Cuntz–Krieger quotient is its Leavitt path algebra.
Sarrazola-Alzate Andrés +4 more
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Signed Total Roman Domination in Digraphs
Discussiones Mathematicae Graph Theory, 2017 Let D be a finite and simple digraph with vertex set V (D). A signed total Roman dominating function (STRDF) on a digraph D is a function f : V (D) → {−1, 1, 2} satisfying the conditions that (i) ∑x∈N−(v)f(x) ≥ 1 for each v ∈ V (D), where N−(v) consists ...
Volkmann Lutz
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Path homology theory of edge-colored graphs
Open Mathematics, 2021 In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau.
Muranov Yuri V., Szczepkowska Anna
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, 1991 International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 3, Page 579-586, 1993.
Garry Johns, Karen Sleno
wiley +1 more source
Volume inequalities for flow polytopes of full directed acyclic graphs [PDF]
Given a finite directed acyclic graph, the space of non-negative unit flows is a lattice polytope called the flow polytope of the graph. We consider the volumes of flow polytopes for directed acyclic graphs on \(n+1\) vertices with a fixed degree ...
McElroy, James Ford, Braun, Benjamin
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Discussiones Mathematicae Graph Theory, 2018 A digraph is called irregular if its distinct vertices have distinct degree pairs. An irregular digraph is called minimal (maximal) if the removal of any arc (addition of any new arc) results in a non-irregular digraph. It is easily seen that the minimum
Górska Joanna +4 more
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© Hindawi Publishing Corp. AN ALGEBRAIC FRAMEWORK OF WEIGHTED DIRECTED GRAPHS
, 2003 We show that an algebraic formulation of weighted directed graphs leads to in-troducing a k-vector space equipped with two coproducts ∆ and ∆ ̃ verifying the so-called coassociativity breaking equation (∆̃ ⊗ id) ∆ = (id⊗∆)∆̃. Such a space is called an L-
Philippe Leroux
core
On the sum of the total domination numbers of a diagraph and its converse
, 2019 A vertex subset S of a digraph D is called a dominating set of D if every vertex not in S has an in-neighbor in S. A dominating set S of D is called a total dominating set of D if the subdigraph induced by S has no isolated vertices. The total domination
Xie, Zhihong +2 more
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