Open AccessRelationship between adjacency and distance matrix of graph of diameter two
Author(s) -
Siti L. Chasanah,
Elvi Khairunnisa,
Muhammad Yusuf,
Kiki Ariyanti Sugeng
Publication year - 2021
Publication title -
indonesian journal of combinatorics
Language(s) - English
Resource type - Journals
ISSN - 2541-2205
DOI - 10.19184/ijc.2021.5.2.1
Subject(s) - adjacency matrix , graph energy , combinatorics , distance matrix , mathematics , degree matrix , adjacency list , matrix (chemical analysis) , hollow matrix , symmetric matrix , graph , diagonal matrix , integer matrix , nonnegative matrix , discrete mathematics , diagonal , graph power , line graph , physics , eigenvalues and eigenvectors , geometry , materials science , quantum mechanics , composite material
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 .