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This note deals with the relationship between the total number of $k$-walks in a graph, and the sum of the $k$-th powers of its vertex degrees. In particular, it is shown that the the number of all $k...
For a graph G, its rth power G^r has the same vertex set as G, and has an edge between any two vertices within distance r of each other in G. We give a lower bound for the number of edges in the rth p...
A note on the minimum skew rank of powers of paths
minimum skew rank path (strict) power of a graph Combinatorics
2011/9/5
Abstract: The real minimum skew rank of a simple graph G is the smallest possible rank among all real skew symmetric matrices, whose (i,j)-entry (for i not equal to j) is nonzero whenever {i, j} is an...
On the asymptotic distribution of the singular values of powers of random matrices
asymptotic distribution singular values of powers of random matrices
2011/1/21
We consider powers of random matrices with independent entries. Let Xij , i, j ≥ 1,be independent complex random variables with EXij = 0 and E|Xij |2 = 1 and let X denote an n×n matrix with [X]ij = Xi...
Let O be the ring of integers of a non-Archimedean local eld and a xed uniformizer of O. We establish three main results.