TY - JOUR
T1 - Smith Normal Form of Distance Matrix of Block Graphs
AU - Chen , Jing
AU - Hou , Yaoping
JO - Annals of Applied Mathematics
VL - 1
SP - 20
EP - 29
PY - 2022
DA - 2022/06
SN - 32
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/20624.html
KW - block graph, distance matrix, Smith normal form.
AB - <p style="text-align: justify;">A connected graph, whose blocks are all cliques (of possibly varying sizes),
is called a block graph. Let $D(G)$ be its distance matrix. In this note, we prove
that the Smith normal form of $D(G)$ is independent of the interconnection way
of blocks and give an explicit expression for the Smith normal form in the case
that all cliques have the same size, which generalize the results on determinants.</p>