Edge-grafting theorems on permanents of Laplacian matrices of graphs and their applications
نویسندگان
چکیده
The trees, respectively unicyclic graphs, on n vertices with the smallest Laplacian permanent are studied. In this paper, by edge-grafting transformations, the n-vertex trees of given bipartition having the second and third smallest Laplacian permanent are identified. Similarly, the n-vertex bipartite unicyclic graphs of given bipartition having the first, second and third smallest Laplacian permanent are characterized. Consequently, the n-vertex bipartite unicyclic graphs with the first, second and third smallest Laplacian permanent are determined.
منابع مشابه
Edge-grafting Theorems on Permanents of the Laplacian Matrices of Graphs and Their Applications
The trees, respectively unicyclic graphs, on n vertices with the smallest Laplacian permanent are studied. In this paper, by edge-grafting transformations, the n-vertex trees of given bipartition having the second and third smallest Laplacian permanent are identified. Similarly, the n-vertex bipartite unicyclic graphs of given bipartition having the first, second and third smallest Laplacian pe...
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