Topological Properties of Hypercubes
IEEE Transactions on Computers
Embedding trees in recursive circulants
Discrete Applied Mathematics
Recursive circulants and their embeddings among hypercubes
Theoretical Computer Science
The rainbow connectivity of a graph
Networks
The rainbow connection of a graph is (at most) reciprocal to its minimum degree
Journal of Graph Theory
| Hi-index | 0.09 |
A path in an edge-colored graph G, whose adjacent edges may have the same color, is called a rainbow path if no two edges of the path are colored the same. The rainbow connection number rc(G) of G is the minimum integer i for which there exists an i-edge-coloring of G such that every two distinct vertices of G are connected by a rainbow path. The strong rainbow connection number src(G) of G is the minimum integer i for which there exists an i-edge-coloring of G such that every two distinct vertices u and v of G are connected by a rainbow path of length d(u,v). In this paper, we give upper and lower bounds of the (strong) rainbow connection numbers of Cayley graphs on Abelian groups. Moreover, we determine the (strong) rainbow connection numbers of some special cases.