Abstract—Graph polynomials are important objects of research in graph theory. Particularly, the permanental polynomials are widely used in Physics and Chemistry. As the difficulty to evaluate the permanental polynomials, this paper deals with the computation of the permanental polynomials of graphs under various operations. Firstly, we give explicit expressions for the permanental polynomials of single subdivision graphs and bisubdivision graphs in recursive ways, respectively. Then we deduce the permanental polynomials of degree subdivision graphs by the product of matrices. Based on these, the permanental polynomials of those physical graphs and chemical graphs which can be generated by subdivision operations can be derived.

Index Terms—Permanent, permanental polynomial, subdivision graph.

Wei Li is with the Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710129, P. R. China (e-mail: liw@nwpu.edu.cn).

Cite: Wei Li, "The Permanental Polynomials of Subdivision Graphs," International Journal of Applied Physics and Mathematics vol. 4, no. 4, pp. 227-231, 2014.