Zeta functions of line, middle, total graphs of a graph and their coverings

Jin Ho Kwak, Iwao Sato
2006 Linear Algebra and its Applications  
We consider the (Ihara) zeta functions of line graphs, middle graphs and total graphs of a regular graph and their (regular or irregular) covering graphs. Let L(G), M(G) and T (G) denote the line, middle and total graph of G, respectively. We show that the line, middle and total graph of a (regular and irregular, respectively) covering of a graph G is a (regular and irregular, respectively) covering of L(G), M(G) and T (G), respectively. For a regular graph G, we express the zeta functions of
more » ... e line, middle and total graph of any (regular or irregular) covering of G in terms of the characteristic polynomial of the covering. Also, the complexities of the line, middle and total graph of any (regular or irregular) covering of G are computed. Furthermore, we discuss the L-functions of the line, middle and total graph of a regular graph G.
doi:10.1016/j.laa.2006.01.033 fatcat:slg6zgruwnfffndlyvwvy2k3wy