Volume 32, Issue 1
Smith Normal Form of Distance Matrix of Block Graphs

Jing Chen & Yaoping Hou

Ann. Appl. Math., 32 (2016), pp. 20-29.

Published online: 2022-06

Export citation
  • Abstract

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.

  • AMS Subject Headings

05C50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAM-32-20, author = {Chen , Jing and Hou , Yaoping}, title = {Smith Normal Form of Distance Matrix of Block Graphs}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {32}, number = {1}, pages = {20--29}, abstract = {

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.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/20624.html} }
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 -

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.

Chen , Jing and Hou , Yaoping. (2022). Smith Normal Form of Distance Matrix of Block Graphs. Annals of Applied Mathematics. 32 (1). 20-29. doi:
Copy to clipboard
The citation has been copied to your clipboard