THE DETERMINANT OF THE ADJACENCY MATRIX OF CYCLE-POWER GRAPH C4 n

Abstract

Cycle-Power Graphs, Cn d is a graph that has n vertices and two vertices u and v are adjacent if and only if distance between u and v not greater than d. In this paper, we show that the determinant of the adjacency matrix of cycle-power graph Cn 4 are as follows 

det(A(Cn 4)) =
0 ; n ≡ 0, 2, 4, 6, 8 mod 10
8 ; n ≡ 1, 3, 7, 9 mod 10
128 ; n ≡ 5 mod 10.
and the condition for the adjacency matrix of cycle-power graph Cn d is
singular matrix.