On Orthogonal Double Covers of Circulant Graphs
Journal of Advances in Mathematics and Computer Science · pp. 394–401 · Published 7 Nov 2013
10.9734/BJMCS/2014/5999Abstract
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.
Cited by 3
Ahmed El-Mesady, Tasneem Farahat, Ramadan El-Shanawany · Algorithms · 2023
R. El-Shanawany, A. El-Mesady · AKCE International Journal of Graphs and Combinatorics · 2017
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