On Cyclic Orthogonal Double Covers of Circulant Graphs using Infinite Graph Classes
نویسندگان
چکیده
منابع مشابه
General Cyclic Orthogonal Double Covers of Finite Regular Circulant Graphs
An orthogonal double cover (ODC) of a graph H is a collection ( ) { } v G v V H : = ∈ of ( ) V H subgraphs (pages) of H, so that they cover every edge of H twice and the intersection of any two of them contains exactly one edge. An ODC of H is cyclic (CODC) if the cyclic group of order ( ) V H is a subgroup of the automorphism group of . In this paper, we introduce a general orthogonal la...
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Let H = {A1, . . . , An, B1, . . . , Bn} be a collection of 2n subgraphs of the complete bipartite graph Kn,n. The collection H is called an orthogonal double cover (ODC) of Kn,n if each edge of Kn,n occurs in exactly two of the graphs in H; E(Ai) ∩ E(Aj) = φ = E(Bi) ∩ E(Bj) for every i, j ∈ {1, . . . , n} with i = j, and for any i, j ∈ {1, . . . , n}, |E(Ai)∩E(Bj)| = 1. If Ai ∼= G ∼= Bi for al...
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An orthogonal double cover (ODC) of the complete graph Kn by some graph G is a collection of n spanning subgraphs of Kn, all isomorphic to G, such that any two of the subgraphs share exactly one edge and every edge of Kn is contained in exactly two of the subgraphs. A necessary condition for such an ODC to exist is that G has exactly n− 1 edges. We show that for any given positive integer d, al...
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An orthogonal double cover (ODC) of the complete graph Kn by some graph G is a collection of n spanning subgraphs of Kn, all isomorphic to G, such that any two of the subgraphs share exactly one edge and every edge of Kn is contained in exactly two of the subgraphs. A necessary condition for such an ODC to exist is that G has exactly n− 1 edges. We show that for any given positive integer d, al...
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Gronau, Mullin, and Rosa conjectured that for every tree T with n vertices except for P4 there exists an ODC of Kn by T . They also proved the conjecture for all caterpillars of diameter 3. Later, Leck and Leck proved it for all caterpillars of diameter 4 and all trees with up to 14 vertices. We prove the conjecture for all carerpillars of diameter 5 and order n ≥ 24; for orders 15 ≤ n ≤ 23 we ...
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ژورنال
عنوان ژورنال: British Journal of Mathematics & Computer Science
سال: 2013
ISSN: 2231-0851
DOI: 10.9734/bjmcs/2013/4165