Results 11 to 20 of about 2,302 (247)
On the complexity of deciding whether the distinguishing chromatic number of a graph is at most two [PDF]
Discrete Mathematics, 2011 In an article [3] published recently in this journal, it was shown that when k >= 3, the problem of deciding whether the distinguishing chromatic number of a graph is at most k is NP-hard. We consider the problem when k = 2. In regards to the issue of solvability in polynomial time, we show that the problem is at least as hard as graph automorphism ...
Chinh Hoang, R Sritharan
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Some Equal Degree Graph Edge Chromatic Number [PDF]
MATEC Web of Conferences, 2016 Let G(V, E) be a simple graph and k is a positive integer, if it exists a mapping of f, and satisfied with f(e1)≠6 = f(e2) for two incident edges e1,e2∉E(G), f(e1)≠6=f(e2), then f is called the k-proper-edge coloring of G(k-PEC for short).
Liu Jun +4 more
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Adjacent Vertex Distinguishing Coloring of Fuzzy Graphs [PDF]
Mathematics, 2023 In this paper, we consider the adjacent vertex distinguishing proper edge coloring (for short, AVDPEC) and the adjacent vertex distinguishing total coloring (for short, AVDTC) of a fuzzy graph.
Zengtai Gong, Chen Zhang
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Neighbor Sum Distinguishing Total Chromatic Number of Planar Graphs without 5-Cycles [PDF]
Discussiones Mathematicae Graph Theory, 2020 For a given graph G = (V (G), E(G)), a proper total coloring ϕ: V (G) ∪ E(G) → {1, 2, . . . , k} is neighbor sum distinguishing if f(u) ≠ f(v) for each edge uv ∈ E(G), where f(v) = Σuv∈E(G) ϕ(uv)+ϕ(v), v ∈ V (G). The smallest integer k in such a coloring
Zhao Xue, Xu Chang-Qing
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Distinguishing chromatic number of Hamiltonian circulant graphs [PDF]
, 2023 The distinguishing chromatic number of a graph $G$ is the smallest number of colors needed to properly color the vertices of $G$ so that the trivial automorphism is the only symmetry of $G$ that preserves the coloring. We investigate the distinguishing chromatic number for Hamiltonian circulant graphs with maximum degree at most 4.
Barrus, Michael D. +2 more
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Neighbor Distinguishing Colorings of Graphs with the Restriction for Maximum Average Degree [PDF]
Axioms, 2023 Neighbor distinguishing colorings of graphs represent powerful tools for solving the channel assignment problem in wireless communication networks. They consist of two forms of coloring: neighbor distinguishing edge coloring, and neighbor distinguishing ...
Jingjing Huo +3 more
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General Vertex-Distinguishing Total Coloring of Graphs [PDF]
Journal of Applied Mathematics, 2014 The general vertex-distinguishing total chromatic number of a graph G is the minimum integer k, for which the vertices and edges of G are colored using k colors such that any two vertices have distinct sets of colors of them and their incident edges.
Chanjuan Liu, Enqiang Zhu
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Upper Bounds for the List-Distinguishing Chromatic Number [PDF]
Graphs and CombinatoricsAbstract In this paper, all results apply only to finite graphs. Let G be a simple connected finite graph with n vertices and maximum degree $$\Delta (G)$$ Δ ( G )
Amitayu Banerjee +2 more
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General neighbour-distinguishing index via chromatic number [PDF]
Discrete Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mirko Hornák, Roman Soták
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Vertex-Distinguishing IE-Total Colorings of Complete Bipartite Graphs Km,N(m < n) [PDF]
Discussiones Mathematicae Graph Theory, 2013 Let G be a simple graph. An IE-total coloring f of G is a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. Let C(u) be the set of colors of vertex u and edges incident to u under f. For an IE-total coloring
Chen Xiang’en, Gao Yuping, Yao Bing
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