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 v i and for the number of v i − v j paths of lengths 3 and 4 in a simple graph G, in terms of the adjacency matrix and with the helps of combinatorics.
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