On Cartesian Products of Orthogonal Double Covers

Abstract

Let be a graph on vertices and G a collection of subgraphs of , one for each vertex, where G is an orthogonal double cover (ODC) of if every edge of occurs in exactly two members of G and any two members share an edge whenever the corresponding vertices are adjacent in and share no edges whenever the corresponding vertices are nonadjacent in . In this paper, we are concerned with the Cartesian product of symmetric starter vectors of orthogonal double covers of the complete bipartite graphs and using this method to construct ODCs by new disjoint unions of complete bipartite graphs.

The <i>g</i>-Good-Neighbor Connectivity of Some Cartesian Product Graphs

“…In fact, many well-known networks can be constructed by the Cartesian products of some simple graphs and the Cartesian product preserves many nice properties such as regularity, existence of Hamilton cycles and Euler circuits, and transitivity of the initial graphs. See [11] [12] [13].…”

Orthogonal double cover of Complete Bipartite Graph by disjoint union of complete bipartite graphs

“…The following theorem of El-Shanawany et al [6] relates the ODCs of complete bipartite graphs and the Cartesian product of two symmetric starter vectors.…”

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