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Showing 1 to 4 of 4 for “"Path cover"”.
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On the minimum rank of certain graphs with path cover number 2
… of a graph. We define a family of graphs with path cover number two and consider restrictions on the structure and minimum rank of these types of graphs. We consider a sub-family of these graphs and calculate the zero-forcing number and the positive semidefinite minimum rank. We also conjecture …
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The Relationship Between the Minimal Rank of a Tree and the Rank-Spreads of the Vertices and Edges
… well-known result that for a tree the sum of its path cover number and minimal rank is equal to the number of vertices in the tree. The rank-spread of a vertex v of G is the difference between the minimal ranks of G and G - v, the graph obtained by deleting v and all its incident edges from G. The …
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Matchings, Connectivity, and Eigenvalues in Regular Graphs
… including the Chinese postman problem, the path cover number, the average edge-connectivity, and the number of perfect matchings. In Chapter 5, we study an $r$-dynamic coloring problem and give the relationship between the $r$-dynamic chromatic number and the chromatic number in regular …