## Ars Combinatoria, Volume 74Department of Combinatorics and Optimization, University of Waterloo., 2005 - Combinatorial analysis |

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### Contents

Ranks of Regular Graphs Under Certain Unary Operations | 3 |

Resolving Edge Colorings in Graphs by G Chartrand V Saenpholphat | 33 |

Multistar Decomposition of Complete Multigraphs by HungChih Lee | 49 |

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18 other sections not shown

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3-connected 7r is potentially a-b walk A-vertices adjacent assume Cartesian product Cayley graph combinatorial common neighbours complete graph components conjecture connected graph consider construction Corollary coset critical graph cube-free defined degree sequence denote digraph Discrete Math disjoint dominating set domination graph domination number dual graph Ec(G edge chromatic edge coloring EG(a eigenvalues exists finite follows from Lemma G and H G contains graph G Graph Theory graphic sequence Hence implies independence number independent set induced initial blocks integer isomorphic least Lemma length Let G let H lower bound matrix maximal multistars neighbors nonzero oriented graph pair parallel classes partition permutation permutation graph positive integer Proof Proposition prove regular graph residual sequence resolving edge coloring result subgraph subgroup H subset Suppose Theorem 2.2 tournament vertex set vertex transitive vertices voltage x-y walk Xre(G zero eigenvalues