# On the number of paths of length 5 in a graph

## DOI:

https://doi.org/10.14419/ijamr.v4i1.3874## Published:

2015-01-04## Keywords:

Adjacency Matrix, Cycle, Graph Theory, Path, Subgraph, Walk.## Abstract

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 each of which starts from a specific vertex \(v_{i}\) and for the number of \(v_{i}-v_{j}\) paths of length 5 in a simple graph G, in terms of the adjacency matrix and with the help of combinatorics.## References

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