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| SMITH NORMAL FORMAL OF DISTANCE MATRIX OF BLOCK GRAPHS |
| Jing Chen,Yaoping Hou |
| (The center of discrete mathematics, Fuzhou University, Fujian 350003, PR China;School of Mathematics, Hunan First Normal University, Hunan 410205, PR of China) |
| DOI： |
| 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. |
| Key words: block graph; distance matrix; Smith normal form |