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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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Arboricity and span in fuzzy chromatic index
Ratio Mathematica, 2022 A fuzzy matching is a set of edges in which an edge does not incident on a vertex with same membership value. If every vertex of fuzzy graph is M-Plunged then the fuzzy matching is called as fair fuzzy matching.
S. Yahya Mohamed, S. Suganthy
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Journal of Graph Theory, 2012 AbstractThe star chromatic index of a graph G is the minimum number of colors needed to properly color the edges of the graph so that no path or cycle of length four is bi‐colored. We obtain a near‐linear upper bound in terms of the maximum degree . Our best lower bound on in terms of Δ is valid for complete graphs. We also consider the special case
Dvořák, Zdeněk +2 more
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Discrete Mathematics, 2004 Given positive integers \(k,d,\;k \geq 2d\), a \((k,d)\)-edge coloring of a graph \(G\) is a mapping \(c:\;E(G) \to \{0,1,\dots, k-1\}\) such that \(d \leq | c(e_i) - c(e_j)| \leq k-d\) whenever two edges \(e_i,e_j\) are adjacent. The authors introduce the circular chromatic index \(\chi_c'(G)\) defined as \(\chi_c'(G) = \inf\{\frac{k}{d}:\;G\) has a \(
Hackmann, Andrea, Kemnitz, Arnfried
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AVD proper edge-coloring of some families of graphs
International Journal of Mathematics for Industry, 2021 Adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for the proper edge-coloring of [Formula: see text] in which no two adjacent vertices are incident to edges colored with the same set of colors.
J. Naveen
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Steiner Triple Systems with High Chromatic Index [PDF]
SIAM Journal on Discrete Mathematics, 2017 It is conjectured that every Steiner triple system of order $v \neq 7$ has chromatic index at most $(v+3)/2$ when $v \equiv 3 \pmod{6}$ and at most $(v+5)/2$ when $v \equiv 1 \pmod{6}$. Herein, we construct a Steiner triple system of order $v$ with chromatic index at least $(v+3)/2$ for each integer $v \equiv 3 \pmod{6}$ such that $v \geq 15$, with ...
Bryant, Darryn +3 more
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Coloring decompositions of complete geometric graphs [PDF]
, 2019 A decomposition of a non-empty simple graph $G$ is a pair $[G,P]$, such that $P$ is a set of non-empty induced subgraphs of $G$, and every edge of $G$ belongs to exactly one subgraph in $P$.
Huemer, Clemens +2 more
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The Circular Chromatic Index of Flower Snarks [PDF]
The Electronic Journal of Combinatorics, 2006 We determine the circular chromatic index of flower snarks, by showing that $\chi'_c(F_{3})=7/2$, $\chi'_c(F_{5})=17/5$ and $\chi'_c(F_{k})=10/3$ for every odd integer $k\ge 7$, where $F_k$ denotes the flower snark on $4k$ vertices.
Ghebleh, Mohammad +3 more
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A Complexity Measure for Continuous Time Quantum Algorithms [PDF]
, 2000 We consider unitary dynamical evolutions on n qubits caused by time dependent pair-interaction Hamiltonians and show that the running time of a parallelized two-qubit gate network simulating the evolution is given by the time integral over the chromatic ...
B. Bollobás +11 more
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Acyclic, Star and Oriented Colourings of Graph Subdivisions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let G be a graph with chromatic number χ (G). A vertex colouring of G is \emphacyclic if each bichromatic subgraph is a forest. A \emphstar colouring of G is an acyclic colouring in which each bichromatic subgraph is a star forest. Let χ _a(G) and χ _s(G)
David R. Wood
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