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On the distance matrix of a directed graph
Author(s) -
Graham R. L.,
Hoffman A. J.,
Hosoya H.
Publication year - 1977
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190010116
Subject(s) - mathematics , combinatorics , graph , matrix (chemical analysis) , distance matrix , directed graph , discrete mathematics , composite material , materials science
In this note, we show how the determinant of the distance matrix D(G ) of a weighted, directed graph G can be explicitly expressed in terms of the corresponding determinants for the (strong) blocks G i of G . In particular, when cof D(G ), the sum of the cofactors of D(G ), does not vanish, we have the very attractive formula.