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Full-Text Articles in Physical Sciences and Mathematics
Packings And Coverings Of Complete Graphs With A Hole With The 4-Cycle With A Pendant Edge, Yan Xia
Packings And Coverings Of Complete Graphs With A Hole With The 4-Cycle With A Pendant Edge, Yan Xia
Electronic Theses and Dissertations
In this thesis, we consider packings and coverings of various complete graphs with the 4-cycle with a pendant edge. We consider both restricted and unrestricted coverings. Necessary and sufficient conditions are given for such structures for (1) complete graphs Kv, (2) complete bipartite graphs Km,n, and (3) complete graphs with a hole K(v,w).
Restricted And Unrestricted Coverings Of Complete Bipartite Graphs With Hexagons, Wesley M. Surber
Restricted And Unrestricted Coverings Of Complete Bipartite Graphs With Hexagons, Wesley M. Surber
Electronic Theses and Dissertations
A minimal covering of a graph G with isomorphic copies of graph H is a set {H1, H2, H3, ... , Hn} where Hi is isomorphic to H, the vertex set of Hi is a subset of G, the edge set of G is a subset of the union of Hi's, and the cardinality of the union of Hi's minus G is minimum. Some studies have been made of covering the complete graph in which case an added condition of the edge set of Hi …