منابع مشابه
Edge-Distinguishing Index of a Graph
We introduce a concept of edge-distinguishing colourings of graphs. A closed neighbourhood of an edge e ∈ E(G) is a subgraph N [e] induced by the edge e and all the edges adjacent to it. We say that a colouring c : E(G) → C distinguishes two edges e1 and e2 if there does not exist an isomorphism φ of N [e1] onto N [e2] such that φ(e1) = e2, and φ preserves colours of c. An edge-distinguishing i...
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The distinguishing number (resp. index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling (resp. edge labeling) with $d$ labels that is preserved only by a trivial automorphism. For any $n in mathbb{N}$, the $n$-subdivision of $G$ is a simple graph $G^{frac{1}{n}}$ which is constructed by replacing each edge of $G$ with a path of length $n$...
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An adjacent vertex distinguishing edge-coloring or an avd-coloring of a simple graph G is a proper edge-coloring of G such that no pair of adjacent vertices meets the same set of colors. We prove that every graph with maximum degree ∆ and with no isolated edges has an avd-coloring with at most ∆ + 300 colors, provided that ∆ > 1020. AMS Subject Classification: 05C15
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2017
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2017.02.032