This paper introduces a new class of graphs, the clique paths (or the CP graphs), and shows that their distance determinant and distance inertia are independent of their structures. The CP graphs include the family of linear $2$-trees. When a graph is attached to a CP graph, it is shown that the distance determinant and the distance inertia are also independent of the structure of the CP graph. Applications to the addressing problem proposed by Graham and Pollak in 1971 are given.
@article{10_37236_8014,
author = {Yen-Jen Cheng and Jephian C.-H. Lin},
title = {Graph families with constant distance determinant},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {4},
doi = {10.37236/8014},
zbl = {1401.05181},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8014/}
}
TY - JOUR
AU - Yen-Jen Cheng
AU - Jephian C.-H. Lin
TI - Graph families with constant distance determinant
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/8014/
DO - 10.37236/8014
ID - 10_37236_8014
ER -
%0 Journal Article
%A Yen-Jen Cheng
%A Jephian C.-H. Lin
%T Graph families with constant distance determinant
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/8014/
%R 10.37236/8014
%F 10_37236_8014
Yen-Jen Cheng; Jephian C.-H. Lin. Graph families with constant distance determinant. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/8014
