摘要
Let LE(G) denote the Laplacian energy of a graph G. In this paper the xyz-transformations G^(xyz) of an r-regular graph G for x,y,z∈{0,1, +,-} are considered. The explicit formulas of LE(G^(xyz)) are presented in terms of r,the number of vertices of G for any positive integer r and x,y,z∈{ 0,1},and also for r = 2 and all x,y,z∈{0,1,+,-}. Some Laplacian equienergetic pairs of G^(xyz) for r = 2 and x,y,z∈{0,1, +,-} are obtained. This also provides several ways to construct infinitely many pairs of Laplacian equienergetic graphs.
Let LE（G） denote the Laplacian energy of a graph G. In this paper the xyz-transformations G^（xyz） of an r-regular graph G for x,y,z∈{0,1, ＋,-} are considered. The explicit formulas of LE（G^（xyz）） are presented in terms of r,the number of vertices of G for any positive integer r and x,y,z∈{ 0,1},and also for r = 2 and all x,y,z∈{0,1,＋,-}. Some Laplacian equienergetic pairs of G^（xyz） for r = 2 and x,y,z∈{0,1, ＋,-} are obtained. This also provides several ways to construct infinitely many pairs of Laplacian equienergetic graphs.
基金
National Natural Science Foundation of China(No.11371086)
the Fund of Science and Technology Commission of Shanghai Municipality,China(No.13ZR1400100)
