vol9_pp27-31. 115KB Jun 04 2011 12:06:17 AM
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A limiting formula is given for the spectral radius of the expanded graph when the lengths of some chains replacing the original edges tend to innity.. The proofs depend on
The second smallest eigenvalue (known as algebraic connectivity ) of the Laplacian matrix of an unicyclic graph is very much related to the 3rd smallest eigenvalue of a spanning tree
The authors would like to thank the referee for her/his very careful reading and useful
Weighted graph, Generalized Bethe tree, Laplacian matrix, Adjacency matrix, Spectral radius, Algebraic connectivity.. AMS
Assume that the contrary holds, i.e., suppose that there is a graph G of type-III such that G has the greatest maximum eigenvalue in G( n, ∆).. We consider the next
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
In the case of a partial TP matrix, the graph of whose specified entries is a sym- metrically placed cycle, as given in (1.1), the necessary conditions for a TP completion are the
