Chengzheng Yu
Published 2016-12-15Version 1
The number of walks from one vertex to another in a finite graph can be counted by the adjacency matrix. In this paper, we prove two theorems that connect the graph Laplacian with two types of walks in a graph. By defining two types of walks and giving orientation to a finite graph, one can easily count the number of the total signs of each kind of walk from one element to another with a fixed length.
Comments: 5 pages, 2 figures
The number of ideals of $\mathbb{Z}[x]$ containing $x(x-α)(x-β)$ with given index
Nonpositive Eigenvalues of the Adjacency Matrix and Lower Bounds for Laplacian Eigenvalues
The kernel of the adjacency matrix of a rectangular mesh
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