Results 51 to 60 of about 502 (87)
Characterization of Line-Consistent Signed Graphs
, 2015 The line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is consistent if every circle (cycle, circuit) has positive vertex-sign product. Acharya, Acharya, and Sinha recently characterized line-consistent signed graphs, i.e.
Slilaty, Daniel C., Zaslavsky, Thomas
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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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Eigenvalues of complex unit gain graphs and gain regularity
Special MatricesA complex unit gain graph (or T{\mathbb{T}}-gain graph) Γ=(G,γ)\Gamma =\left(G,\gamma ) is a gain graph with gains in T{\mathbb{T}}, the multiplicative group of complex units.
Brunetti Maurizio
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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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Dualizing Distance-Hereditary Graphs
Discussiones Mathematicae Graph Theory, 2021 Distance-hereditary graphs can be characterized by every cycle of length at least 5 having crossing chords. This makes distance-hereditary graphs susceptible to dualizing, using the common extension of geometric face/vertex planar graph duality to cycle ...
McKee Terry A.
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Union of Distance Magic Graphs
Discussiones Mathematicae Graph Theory, 2017 A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection ℓ from V to the set {1, . . . , n} such that the weight w(x) = ∑y∈NG(x) ℓ(y) of every vertex x ∈ V is equal to the same element μ, called the magic constant.
Cichacz Sylwia, Nikodem Mateusz
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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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Partitioning the vertex set of $G$ to make $G\,\Box\, H$ an efficient open domination graph [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 A graph is an efficient open domination graph if there exists a subset of vertices whose open neighborhoods partition its vertex set. We characterize those graphs $G$ for which the Cartesian product $G \Box H$ is an efficient open domination graph when ...
Tadeja Kraner Šumenjak +3 more
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Orientable ℤN-Distance Magic Graphs
Discussiones Mathematicae Graph Theory, 2019 Let G = (V, E) be a graph of order n. A distance magic labeling of G is a bijection ℓ: V → {1, 2, . . ., n} for which there exists a positive integer k such that ∑x∈N(v)ℓ(x) = k for all v ∈ V, where N(v) is the open neighborhood of v.
Cichacz Sylwia +2 more
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Open Mathematics, 2016 As a generalization of the Sierpiński-like graphs, the subdivided-line graph Г(G) of a simple connected graph G is defined to be the line graph of the barycentric subdivision of G.
Shang Yilun
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