University of Wyoming Open Journals
Not a member yet
3193 research outputs found
Sort by
Edge-grafting theorems on permanents of Laplacian matrices of graphs and their applications
No full textThe trees, respectively unicyclic graphs, on n vertices with the smallest Laplacian permanent are studided. In this paper, by edge-grafting transformations, the n-vertex trees of given pipartitino having the second and the third smallest Laplacian permanent are identified. Similarily, the n-vertex bipartite unicyclic graphs of given bipartition having the first, second and third smallest Lapalacian permanent are characterized. Consequently, the n-vertex bipartite unicyclic graphs with the first, second and third smallest Laplacian permanent are determined
Notes on an Anderson-Taylor type inequality
No full textAs a complement to Olkin's extension of Anderson-Taylor's trace inequality, the following inequality is proved:
where the inequality is in the sense of Loewner partial order and Ai, i+1,...,n, are positive definite matrices. Some related results for M-matrices are also discussed
Maxima of the Q-index:graphs with bounded clique number
No full textThis paper gives a tight upper bound on the spectral radius of the signless Laplacian of graphs of given order and clique number. More precisely, let G be a graph of order n, let A be its adjacency matrix, and let D be the diagonal matrix of the row-sums of A. If G has clique number ω, then the largest eigenvalue q(G) of the matrix Q=A=D satisfies
q(G)≤ 2(1-1/ω)n
If G is a complete regular ω-partite graph, then equality holds in the above inequality. 
