The Edge Product of Networks

In this paper, a new graph product, called Edge Graph Product (EGP) is proposed by replacing each edge in the multiplicand graph by a copy of the multiplier graph via two candidate nodes. The edge product, unlike other products already proposed, results in a graph whose number of edges is numerical product of the number of the edges in the multiplicand and multiplier graphs, and the number of vertices is not equal to the numerical product of the number of vertices in the multiplicand and multiplier graphs. After formal definition of the new product, some basic properties of the product operator are studied. We then address Hamiltonian, Eulerian and routing properties of the new product, and we show that some of the recently proposed topologies fall within the family of edge product graphs.