Spectra and elementary cycles of the digraphs with unique paths of fixed length
A digraph \(G\), whose adjacency matrix \(A\) satisfies \(A^k= J_n- I_n\), where \(J_n\) is the \(n\times n\) matrix of all ones, is called a digraph with unique paths of fixed length \(k\), shortly UPFL-\(k\) digraph. The authors prove that the UPFL-\(k\) digraphs of the ame order are cospectral and have the same number of elementary cycles of length \(l\) for each \(l\leq k\). This result is a serious generalization of a previous result. The authors also give interesting computational approaches useful in this area.
scientific article; zbMATH DE number 1398466