Abstract
In this paper, we provide an explicit formula for the rank of the walk matrix of the extended Dynkin graph D˜n. Moreover, we prove that the Smith normal form of the walk matrix of the extended Dynkin graph D˜n is{diag(1,…,1︸r−1,n−12,0,…,0),ifnis odd,diag(1,…,1︸r−1,n−1,0,…,0),ifnis even, where r=⌊n2⌋.
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