Number of cycles of small length in a graph
Sasmita Barik, Sane Umesh Reddy · AKCE International Journal of Graphs and Combinatorics · 2023
Let G be a simple undirected graph. In this article, we obtain an explicit formula for the number of 8-cycles in G in terms of the entries of its adjacency matrix. We provide new formulae to find the number of cycles of length 4, 5 and 6 in G. When the girth of G is 10 (resp. 12), an explicit formula for the number of cycles of length 10 (resp. 12) is given. New formulae to find the number of paths of length 3, 4 and 5 in G are also obtained.