The higher-order matching polynomial of a graph

Oswaldo Araujo, Mario Estrada, Daniel A. Morales, Juan Rada
2005 International Journal of Mathematics and Mathematical Sciences  
Given a graphGwithnvertices, letp(G,j)denote the number of waysjmutually nonincident edges can be selected inG. The polynomialM(x)=∑j=0[n/2](−1)jp(G,j)xn−2j, called the matching polynomial ofG, is closely related to the Hosoya index introduced in applications in physics and chemistry. In this work we generalize this polynomial by introducing the number of disjoint paths of lengtht, denoted bypt(G,j). We compare this higher-order matching polynomial with the usual one, establishing similarities
more » ... nd differences. Some interesting examples are given. Finally, connections between our generalized matching polynomial and hypergeometric functions are found.
doi:10.1155/ijmms.2005.1565 fatcat:ybpnjbn7vzg2xcwgdxlu64pu74