vol18_pp530-563. 600KB Jun 04 2011 12:06:04 AM
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Call a graph k -critical if it is minimal (w.r.t. vertex deletion) of rank larger than k.. Clearly, G k is characterized by the k -critical graphs as forbidden
We note that each of the graphs with structures described above can be obtained from certain simple corona graphs by deleting two specific pendant vertices with distance 3..
In this paper we show in Section 2 that the disjoint union of complete graphs without isolated vertex is determined by its Laplacian spectrum in the family of graphs without
The next lemma implies that the final bound in (2.4) will not be helpful if non- negative weight matrices are used for graphs that have small maximum independent sets and vertices
The tree cover number of a multigraph G, denoted T (G), is the minimum number of vertex disjoint simple trees occurring as induced subgraphs of G that cover all of the vertices of
Our second con- struction produces a ( −J )-type tournament matrix from two minimum rank tourna- ment matrices of even orders..
In [6], the author characterized the extremal graph of bicyclic graphs with k pendant vertices with maximal signless Laplacian spectral radius2. For further details, we refer the
In this section, we will use our results on the inertia sets of connected minimum rank 2 graphs and our results on the structure of these minimum rank matrices to investigate
