JOURNAL OF SCIENCE AND ARTS, no.2, pp.371-374, 2018 (ESCI)
Let G be a simple graph of order n. Let c = a + b root m and (c)over-bar = a - b root m, where a and b are two nonzero integers and m is a positive integer such that m is not a perfect square. Let P-L(G) (lambda) = vertical bar lambda I - L(G)vertical bar is denote the Laplacian characteristic polynomial of a graph G. In this study we define that L-c = [l(ij)(c)] is the conjugate Laplacian matrix of the graph G and define that P-L(G)(c) (lambda) = vertical bar(lambda)I - L-c(G)vertical bar is called the conjugate Laplacian characteristic polynomial of a graph G and study their properties.