On the Number of Paths of Lengths 3 and 4 in a Graph

Abstract

In this paper, we obtain explicit formulae for the total number of paths of lengths 3 and 4 in a simple graph G. We also determine some formulae for the number of paths of lengths 3 and 4 each of which starts from an specific vertex vi and for the number of vi-vj paths of lengths 3 and 4 in a simple graph G, in terms of the adjacency matrix and with the helps of combinatorics. Keywords: Adjacency Matrix, Cycle, Graph Theory, Path, Subgraph, Walk .