Results 21 to 30 of about 16,459 (227)
Nordhaus-Gaddum Theorem for the Distinguishing Chromatic Number [PDF]
The Electronic Journal of Combinatorics, 2013 Nordhaus and Gaddum proved, for any graph $G$, that $\chi(G) + \chi(\overline{G}) \leq n + 1$, where $\chi$ is the chromatic number and $n=|V(G)|$. Finck characterized the class of graphs, which we call NG-graphs, that satisfy equality in this bound. In this paper, we provide a new characterization of NG-graphs, based on vertex degrees, which yields a ...
Collins, Karen L., Trenk, Ann
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Adjacent vertex distinguishing acyclic edge coloring of the Cartesian product of graphs [PDF]
Transactions on Combinatorics, 2017 Let $G$ be a graph and $chi^{prime}_{aa}(G)$ denotes the minimum number of colors required for an acyclic edge coloring of $G$ in which no two adjacent vertices are incident to edges colored with the same set of colors. We prove a general bound for $
Fatemeh Sadat Mousavi, Massomeh Noori
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The chromatic distinguishing index of certain graphs
AKCE International Journal of Graphs and Combinatorics, 2020 The distinguishing index of a graph , denoted by , is the least number of labels in an edge coloring of not preserved by any non-trivial automorphism. The distinguishing chromatic index of a graph is the least number such that has a proper edge coloring ...
Saeid Alikhani, Samaneh Soltani
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On multiset colorings of generalized corona graphs [PDF]
Mathematica Bohemica, 2016 A vertex $k$-coloring of a graph $G$ is a \emph{multiset $k$-coloring} if $M(u)\neq M(v)$ for every edge $uv\in E(G)$, where $M(u)$ and $M(v)$ denote the multisets of colors of the neighbors of $u$ and $v$, respectively. The minimum $k$ for which $G$ has
Yun Feng, Wensong Lin
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Distinguishing homomorphisms of infinite graphs [PDF]
, 2012 We supply an upper bound on the distinguishing chromatic number of certain infinite graphs satisfying an adjacency property. Distinguishing proper $n$-colourings are generalized to the new notion of distinguishing homomorphisms. We prove that if a graph $
Bonato, Anthony, Delic, Dejan
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The harmonious chromatic number of almost all trees [PDF]
, 1995 A harmonious colouring of a simple graph G is a proper vertex colouring such that each pair of colours appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colours in such a colouring.For any positive integer ...
Edwards +4 more
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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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Distinguishing chromatic number of Hamiltonian circulant graphs
, 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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Locally identifying coloring in bounded expansion classes of graphs [PDF]
, 2012 A proper vertex coloring of a graph is said to be locally identifying if the sets of colors in the closed neighborhood of any two adjacent non-twin vertices are distinct.
Gonçalves, Daniel +2 more
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Order Quasisymmetric Functions Distinguish Rooted Trees [PDF]
, 2017 Richard P. Stanley conjectured that finite trees can be distinguished by their chromatic symmetric functions. In this paper, we prove an analogous statement for posets: Finite rooted trees can be distinguished by their order quasisymmetric functions ...
Hasebe, Takahiro, Tsujie, Shuhei
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