On The Determinant of q-Distance Matrix of a Graph

Hong-Hai Li, Li Su, and Jing Zhang. "On The Determinant of q-Distance Matrix of a Graph." Discussiones Mathematicae Graph Theory 34.1 (2014): 103-111. <http://eudml.org/doc/267842>.

@article{Hong2014,
abstract = {In this note, we show how the determinant of the q-distance matrix Dq(T) of a weighted directed graph G can be expressed in terms of the corresponding determinants for the blocks of G, and thus generalize the results obtained by Graham et al. [R.L. Graham, A.J. Hoffman and H. Hosoya, On the distance matrix of a directed graph, J. Graph Theory 1 (1977) 85-88]. Further, by means of the result, we determine the determinant of the q-distance matrix of the graph obtained from a connected weighted graph G by adding the weighted branches to G, and so generalize in part the results obtained by Bapat et al. [R.B. Bapat, S. Kirkland and M. Neumann, On distance matrices and Laplacians, Linear Algebra Appl. 401 (2005) 193- 209]. In particular, as a consequence, determinantal formulae of q-distance matrices for unicyclic graphs and one class of bicyclic graphs are presented.},
author = {Hong-Hai Li, Li Su, Jing Zhang},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {q-distance matrix; determinant; weighted graph; directed graph; -distance matrix},
language = {eng},
number = {1},
pages = {103-111},
title = {On The Determinant of q-Distance Matrix of a Graph},
url = {http://eudml.org/doc/267842},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Hong-Hai Li
AU - Li Su
AU - Jing Zhang
TI - On The Determinant of q-Distance Matrix of a Graph
JO - Discussiones Mathematicae Graph Theory
PY - 2014
VL - 34
IS - 1
SP - 103
EP - 111
AB - In this note, we show how the determinant of the q-distance matrix Dq(T) of a weighted directed graph G can be expressed in terms of the corresponding determinants for the blocks of G, and thus generalize the results obtained by Graham et al. [R.L. Graham, A.J. Hoffman and H. Hosoya, On the distance matrix of a directed graph, J. Graph Theory 1 (1977) 85-88]. Further, by means of the result, we determine the determinant of the q-distance matrix of the graph obtained from a connected weighted graph G by adding the weighted branches to G, and so generalize in part the results obtained by Bapat et al. [R.B. Bapat, S. Kirkland and M. Neumann, On distance matrices and Laplacians, Linear Algebra Appl. 401 (2005) 193- 209]. In particular, as a consequence, determinantal formulae of q-distance matrices for unicyclic graphs and one class of bicyclic graphs are presented.
LA - eng
KW - q-distance matrix; determinant; weighted graph; directed graph; -distance matrix
UR - http://eudml.org/doc/267842
ER -