The Algebraic Connectivity Of Bicycle Graph Of The Sort

Let G =(V, E) be a simple connected graph, Its vertex set1 2() {,,, }nV G =v v Lv and edge set1 2() {,,, }mE G =e e Le,()()ijA G =a and1 2()(,,,)nD G =diag d d Ld for adjacency matrix and degree diagonal matrix of graph G respectively, Among themid for vertex degree ofiv,Wheniv andjv adjacent, 1ija =; Wheniv andjv nonadjacent,0ija =. L(G) =D(G) -A(G) for Laplacian matrix of graph G,Easy to know L(G) is a positive semi-definite real symmetric singular matrix, let characteristic value of L(G) from big to small arrangement is as follows:1 2 1()()()() 0n nlG lG lG lG-3 3L3 3 =.Because1() 0nlG-> if and only if graph G is a connected graph, so1()nlG-is the algebraic connectivity of G.If m =n +1, graph G be a bicycle graph. If the graph contains two cycles one and only one public vertex, says the graph is tangent bicycle graph; If the graph contains two cycles and have no public vertex, says the graph is disjoint bicycle graph; If the graph contains two cycles at least two public vertex, says the graph is intersect bicycle graph. In this paper, For tangent bicycle graph, we present the first to sixth largest value of algebraic connectivity together with the corresponding graph; For disjoint bicycle graph, we present the first to fourteenth largest value of algebraic connectivity together with the corresponding graph; For intersect bicycle graph, we present the fifth to tenth largest value of algebraic connectivity together with the corresponding graph.