Replacement product

In graph theory, the replacement product of two graphs is a graph product that can be used to reduce the degree of a graph while maintaining its connectivity.

Suppose G is a d-regular graph and H is an e-regular graph with vertex set {0, …, d − 1}. Let R denote the replacement product of G and H. The vertex set of R is the Cartesian product V(G) × V(H). For each vertex u in V(G) and for each edge (i, j) in E(H), the vertex (u, i) is adjacent to (u, j) in R. Furthermore, for each edge (u, v) in E(G), if v is the ith neighbor of u and u is the jth neighbor of v, the vertex (u, i) is adjacent to (v, j) in R.

单词	Replacement product
释义	Replacement product 英语百科 Replacement product In graph theory, the replacement product of two graphs is a graph product that can be used to reduce the degree of a graph while maintaining its connectivity. Suppose G is a d-regular graph and H is an e-regular graph with vertex set {0, …, d − 1}. Let R denote the replacement product of G and H. The vertex set of R is the Cartesian product V(G) × V(H). For each vertex u in V(G) and for each edge (i, j) in E(H), the vertex (u, i) is adjacent to (u, j) in R. Furthermore, for each edge (u, v) in E(G), if v is the ith neighbor of u and u is the jth neighbor of v, the vertex (u, i) is adjacent to (v, j) in R.
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