A graph G is two-disjoint-cycle-cover[r_(1),r_(2)]-pancyclic,if for any integer l satisfying r_(1)≤l≤r_(2),there exist two vertex-disjoint cycles C_(1)and C_(2)in G such that the lengths of C_(1)and C_(2)are l and|V...A graph G is two-disjoint-cycle-cover[r_(1),r_(2)]-pancyclic,if for any integer l satisfying r_(1)≤l≤r_(2),there exist two vertex-disjoint cycles C_(1)and C_(2)in G such that the lengths of C_(1)and C_(2)are l and|V(G)|-l,respectively,where|V(G)|denotes the number of vertices in G.More specifically,a graph G is two-disjoint-cycle-cover vertex[r_(1),r_(2)]-pancyclic(resp.edge[r_(1),r_(2)]-pancyclic)if for any two distinct vertices u_(1),u_(2)∈V(G)(resp.two vertex-disjoint edges e_(1),e_(2)∈E(G)),there exist two vertex-disjoint cycles C_(1)and C_(2)in G such that for every integer l satisfying(1)≤l≤r_(2),C_(1)contains u_(1)(resp.e_(1))with length l and C_(2)contains u_(2)(resp.e_(2))with length|V(G)|-l.In this paper,we consider the problem of two-disjoint-cycle-cover pancyclicity of the n-dimensional augmented cube AQ_(n)and obtain the following results:AQ_(n)is two-disjoint-cycle-cover[3,2^(n-1)]-pancyclic for n≥3.Moreover,AQ_(n)is two-disjoint-cycle-cover vertex[3,2^(n-1)]-pancyclic for n≥3,and AQ_(n)is two-disjoint-cycle-cover edge[4,2^(n-1)]-pancyclic for n≥3.展开更多
文摘A graph G is two-disjoint-cycle-cover[r_(1),r_(2)]-pancyclic,if for any integer l satisfying r_(1)≤l≤r_(2),there exist two vertex-disjoint cycles C_(1)and C_(2)in G such that the lengths of C_(1)and C_(2)are l and|V(G)|-l,respectively,where|V(G)|denotes the number of vertices in G.More specifically,a graph G is two-disjoint-cycle-cover vertex[r_(1),r_(2)]-pancyclic(resp.edge[r_(1),r_(2)]-pancyclic)if for any two distinct vertices u_(1),u_(2)∈V(G)(resp.two vertex-disjoint edges e_(1),e_(2)∈E(G)),there exist two vertex-disjoint cycles C_(1)and C_(2)in G such that for every integer l satisfying(1)≤l≤r_(2),C_(1)contains u_(1)(resp.e_(1))with length l and C_(2)contains u_(2)(resp.e_(2))with length|V(G)|-l.In this paper,we consider the problem of two-disjoint-cycle-cover pancyclicity of the n-dimensional augmented cube AQ_(n)and obtain the following results:AQ_(n)is two-disjoint-cycle-cover[3,2^(n-1)]-pancyclic for n≥3.Moreover,AQ_(n)is two-disjoint-cycle-cover vertex[3,2^(n-1)]-pancyclic for n≥3,and AQ_(n)is two-disjoint-cycle-cover edge[4,2^(n-1)]-pancyclic for n≥3.
