A fast graph traversal algorithm for the computer enumeration of P-V paths of benzenoid graphs

Abstract

A computer program with O(p.n) time complexity is developed for the combinatorial enumeration of peak to valley augmenting paths of any n-vertex benzenoid graph with p number of peaks, using sets as its primary data structure. Peaks and valleys are recognized by using a breadth-first labeling procedure. The code computes the P-V matrix whose determinant is the number of Kekule structures of the given graph G. this program can handle very large graphs and takes only a few seconds to compute the P-V matrix of the typical graph even on a personal computer. As the code is very efficient and compact it can be used in any program that calculates the Kekule structure count (KSC) as an intermediate result.