Results 1 to 10 of about 240 (85)
Neighbor Distinguishing Colorings of Graphs with the Restriction for Maximum Average Degree
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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Multi-set neighbor distinguishing 3-edge coloring
Discrete Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Neighbor Product Distinguishing Total Colorings of Planar Graphs with Maximum Degree at least Ten
Discussiones Mathematicae Graph Theory, 2021 A proper [k]-total coloring c of a graph G is a proper total coloring c of G using colors of the set [k] = {1, 2, . . . , k}. Let p(u) denote the product of the color on a vertex u and colors on all the edges incident with u.
Dong Aijun, Li Tong
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Neighbor Sum Distinguishing Total Choosability of IC-Planar Graphs without Theta Graphs Θ2,1,2
Mathematics, 2021 A theta graph Θ2,1,2 is a graph obtained by joining two vertices by three internally disjoint paths of lengths 2, 1, and 2. A neighbor sum distinguishing (NSD) total coloring ϕ of G is a proper total coloring of G such that ∑z∈EG(u)∪{u}ϕ(z)≠∑z∈EG(v)∪{v}ϕ(
Donghan Zhang
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Group twin coloring of graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 For a given graph $G$, the least integer $k\geq 2$ such that for every Abelian group $\mathcal{G}$ of order $k$ there exists a proper edge labeling $f:E(G)\rightarrow \mathcal{G}$ so that $\sum_{x\in N(u)}f(xu)\neq \sum_{x\in N(v)}f(xv)$ for each edge ...
Sylwia Cichacz, Jakub Przybyło
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Neighbor-distinguishing
Discrete Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Baril, Jean-Luc, Togni, Olivier
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On a Total Version of 1-2-3 Conjecture
Discussiones Mathematicae Graph Theory, 2020 A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set {1, . . . , k}. These colors can be used to distinguish adjacent vertices of G. There are many possibilities of such a distinction.
Baudon Olivier +5 more
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Neighbor Sum Distinguishing Total Choosability of IC-Planar Graphs
Discussiones Mathematicae Graph Theory, 2020 Two distinct crossings are independent if the end-vertices of the crossed pair of edges are mutually different. If a graph G has a drawing in the plane such that every two crossings are independent, then we call G a plane graph with independent crossings
Song Wen-Yao +2 more
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An Improved Upper Bound on Neighbor Expanded Sum Distinguishing Index
Discussiones Mathematicae Graph Theory, 2020 A total k-weighting f of a graph G is an assignment of integers from the set {1, . . . , k} to the vertices and edges of G. We say that f is neighbor expanded sum distinguishing, or NESD for short, if Σw∈N(v) (f(vw) + f(w)) differs from Σw∈N(u)(f(uw) + f(
Vučković Bojan
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Neighbor Sum Distinguishing Total Chromatic Number of Planar Graphs without 5-Cycles
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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