Vaznonienė, Gintarė and Pakeltienė, Rasa
(2013)
*Methods for the Assessment of Rural Social Infrastructure Needs.*
European Countryside, 9 (3).
pp. 526-540.
ISSN 1803-8417

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## Abstract

Let X be a graph on n vertices and let B = {P(x) : x ∈ V (X)} be a collection of n subgraphs of X, one for each vertex, B is an orthogonal double cover (ODC) of X if every edge of X occurs in exactly two members of B and any two members share an edge whenever the corresponding vertices are adjacent in X and share no edges whenever the corresponding vertices are nonadjacent in X. The main question is: given the pair (X, G), is there an ODC of X by G? An obvious necessary condition is that X is a regular. In this paper, we are almost exclusively concerned with the starter maps of the orthogonal double covers of cayley graphs and using this method to construct ODCs by a complete bipartite graph, a complete tripartite graph, caterpillar, and a connected union of a cycle and a star whose center vertex belongs to that cycle.

Item Type: | Article |
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Subjects: | OA Open Library > Mathematical Science |

Depositing User: | Unnamed user with email support@oaopenlibrary.com |

Date Deposited: | 14 Jul 2023 11:33 |

Last Modified: | 21 Dec 2023 06:22 |

URI: | http://archive.sdpublishers.com/id/eprint/1104 |