The m-distance matrix D m of a simple connected undirected graph has an important role in computing the distance matrix D of the graph from the powers of the adjacency matrix using Hadamard product. This paper shows that for an undirected tree T with diameter d, {D 0 .D 1 ,. .. , D d } is an orthogonal basis for the space spanned by the binary equivalent matrices of the first d + 1 powers of the adjacency matrix of T and it gives an invertible conversion matrix for finding the m-distance matrix of T using Frobenius inner product on matrices.
Distance matrix of a graph has important applications in the field of hierarchical clustering, phylogenetic analysis, bioinformatics, telecommunication etc. There are nice research works on determinant, characteristic polynomial and eigen values of distance matrices. This paper describes a formula for finding the distance matrix of a simple connected undirected graph from the powers of the adjacency matrix using Hadamard product on matrices.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.