On the number of paths of length 5 in a graph - Movarraei, Nazanin; Boxwala, Samina Abbas (International Journal of Applied Mathematical Research, 2015)
n this paper, we obtain an explicit formula for the total number of paths of length 5 in a simple graph G. We also determine some formulae for the number of paths of length 5 Â each of which starts from a specific vertex \(v_{i}\) and for the number of \(v_{i}-v_{j}\) paths of length 5 Â in a simple graph G, in terms of the adjacency matrix and with the help of combinatorics.
Keywords: Adjacency Matrix; Cycle; Graph Theory; Path; Subgraph; Walk.