Relationship between adjacency and distance matrix of graph of diameter two

Siti L. Chasanah, Elvi Khairunnisa, Muhammad Yusuf, Kiki A. Sugeng


The relationship among every pair of vertices in a graph can be represented as a matrix, such as in adjacency matrix and distance matrix. Both adjacency and distance matrices have the same property. Adjacency and distance matrices are both symmetric matrix with diagonals entries equals to 0.  In this paper, we discuss relationships between adjacency matrix and distance matrix of a graph of diameter two, which is D=2(J-I)-A. From this relationship, we  also determine the value of the determinant matrix A+D and the upper bound of determinant of matrix D.


adjacency matrix, distance matrix, diameter

Full Text:




R. Bapat, Graphs and Matrices, Hindustan Book Agency, Springer, 2010

G. Chatrand, L. Lesniak, P. Zhang.  Graphs and Digraphs, 6th Edition.CRC Press, 2016

F. Harary,   The Determinant of the Adjacency Matrix of a Graph, SIAM Review. 4(1962). No. 3. 202--210.

H. J. Ryser,  Maximal determinant in Combinatorial Investigation, Canad. J. Math. 8(1978), 245--249

P. Krivka,  dan  N. Trinajstic,  On the Distance Polynomial of Graph, Aplikace math., 28(1983), No. 5, 357--363.


  • There are currently no refbacks.

ISSN: 2541-2205

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

View IJC Stats