Global ETD Search
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Showing 1 to 5 of 5 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 …
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Combinatorial optimization and recognition of graph classes with applications to related models
… and proper interval graphs, and especially, path problems on them. These classes of graphs have been extensively studied and they find many applications in several fields and disciplines such as genetics, molecular biology, scheduling, VLSI design, archaeology, and psychology, among others. …