Results 41 to 50 of about 84 (75)
Sufficient Conditions for a Digraph to Admit A (1, ≤ ℓ)-Identifying Code
Discussiones Mathematicae Graph Theory, 2021 A (1, ≤ ℓ)-identifying code in a digraph D is a subset C of vertices of D such that all distinct subsets of vertices of cardinality at most ℓ have distinct closed in-neighbourhoods within C. In this paper, we give some sufficient conditions for a digraph
Balbuena Camino +2 more
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On characteristic and permanent polynomials of a matrix
Special Matrices, 2017 There is a digraph corresponding to every square matrix over ℂ. We generate a recurrence relation using the Laplace expansion to calculate the characteristic and the permanent polynomials of a square matrix.
Singh Ranveer, Bapat R. B.
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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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, 1991 International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 3, Page 579-586, 1993.
Garry Johns, Karen Sleno
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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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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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Solving the kernel perfect problem by (simple) forbidden subdigraphs for digraphs in some families of generalized tournaments and generalized bipartite tournaments [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 A digraph such that every proper induced subdigraph has a kernel is said to be \emph{kernel perfect} (KP for short) (\emph{critical kernel imperfect} (CKI for short) resp.) if the digraph has a kernel (does not have a kernel resp.).
H. Galeana-Sánchez, M. Olsen
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Bounds on the Signed Roman k-Domination Number of a Digraph
Discussiones Mathematicae Graph Theory, 2019 Let k be a positive integer. A signed Roman k-dominating function (SRkDF) on a digraph D is a function f : V (D) → {−1, 1, 2} satisfying the conditions that (i) Σx∈N−[v]f(x) ≥ k for each v ∈ V (D), where N−[v] is the closed in-neighborhood of v, and (ii)
Chen Xiaodan +2 more
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