Results 61 to 70 of about 1,634 (112)
Distinguishing tournaments with small label classes [PDF]
, 2019 A d-distinguishing vertex (arc) labeling of a digraph is a vertex (arc) labeling using d labels that is not preserved by any nontrivial automorphism. Let ρ(T) (ρ′(T)) be the minimum size of a label class in a 2-distinguishing vertex (arc) labeling of a ...
Lozano Bojados, Antoni
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Coverings of Cubic Graphs and 3-Edge Colorability
Discussiones Mathematicae Graph Theory, 2021 Let h:G˜→Gh:\tilde G \to G be a finite covering of 2-connected cubic (multi)graphs where G is 3-edge uncolorable. In this paper, we describe conditions under which G˜\tilde G is 3-edge uncolorable. As particular cases, we have constructed regular and
Plachta Leonid
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The $(k,\ell)$-rainbow index of random graphs [PDF]
, 2013 A tree in an edge colored graph is said to be a rainbow tree if no two edges on the tree share the same color. Given two positive integers $k$, $\ell$ with $k\geq 3$, the \emph{$(k,\ell)$-rainbow index} $rx_{k,\ell}(G)$ of $G$ is the minimum number of ...
Cai, Qingqiong +2 more
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On Proper (Strong) Rainbow Connection of Graphs
Discussiones Mathematicae Graph Theory, 2021 A path in an edge-colored graph G is called a rainbow path if no two edges on the path have the same color. The graph G is called rainbow connected if between every pair of distinct vertices of G, there is a rainbow path.
Jiang Hui +3 more
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On Local Antimagic Chromatic Number of Cycle-Related Join Graphs
Discussiones Mathematicae Graph Theory, 2021 An edge labeling of a connected graph G = (V, E) is said to be local antimagic if it is a bijection f : E → {1, . . ., |E|} such that for any pair of adjacent vertices x and y, f+(x) ≠ f+(y), where the induced vertex label f+(x) = Σf(e), with e ranging ...
Lau Gee-Choon, Shiu Wai-Chee, Ng Ho-Kuen
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Coloring subgraphs with restricted amounts of hues
Open Mathematics, 2017 We consider vertex colorings where the number of colors given to specified subgraphs is restricted. In particular, given some fixed graph F and some fixed set A of positive integers, we consider (not necessarily proper) colorings of the vertices of a ...
Goddard Wayne, Melville Robert
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The Distinguishing Number and Distinguishing Index of the Lexicographic Product of Two Graphs
Discussiones Mathematicae Graph Theory, 2018 The distinguishing number (index) D(G) (D′(G)) of a graph G is the least integer d such that G has a vertex labeling (edge labeling) with d labels that is preserved only by the trivial automorphism.
Alikhani Saeid, Soltani Samaneh
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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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2-Distance Colorings of Integer Distance Graphs
Discussiones Mathematicae Graph Theory, 2019 A 2-distance k-coloring of a graph G is a mapping from V (G) to the set of colors {1,. . ., k} such that every two vertices at distance at most 2 receive distinct colors.
Benmedjdoub Brahim +2 more
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Facial Rainbow Coloring of Plane Graphs
Discussiones Mathematicae Graph Theory, 2019 A vertex coloring of a plane graph G is a facial rainbow coloring if any two vertices of G connected by a facial path have distinct colors. The facial rainbow number of a plane graph G, denoted by rb(G), is the minimum number of colors that are necessary
Jendroľ Stanislav, Kekeňáková Lucia
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