On the Edge-forwarding Indices of Frobenius Graphs

A G-Frobenius graph Γ,as defined by Fang,Li,and Praeger,is a connected orbital graph ofa Frobenius group G=K H with Frobenius kernel K and Frobenius complement H.Γ is also shownto be a Cayley graph,Γ=Cay(K,S)for K and some subset S of the group K.On the other hand,a network N with a routing function R,written as(N,R),is an undirected graph N together with arouting R which consists of a collection of simple paths connecting every pair of vertices in the graph.The edge-forwarding index π(N)of a network(N,R),defined by Heydemann,Meyer,and Sotteau,isa parameter to describe the maximum load of edges of N.In this paper,we study the edge-forwardingindices of Frobenius graphs.In particular,we obtain the edge-forwarding index of a G-Frobenius graphΓ with rank(G)≤50.