Two disjoint cycles of various lengths in alternating group graph

Alternating group graph has been widely studied recent years because it possesses many good properties. For a graph G, the two-disjoint-cycle-cover [r(1), r(2)]-pancyclicity refers that it contains cycles C-1 and C-2, where V(C-1) boolean AND V (C-2) = empty set, l(C-1) + l(C-2) = vertical bar V(G)vertical bar and r(1) <= l(C-1) <= r(2). In this paper, it is proved that the n-dimensional alternating group graph AG(n) is two-disjoint-cycle-cover [3, n!/4]-pancyclic, where n >= 4. (C) 2022 Elsevier Inc. All rights reserved.

Automated summary

The alternating group graph has been extensively studied in recent years due to its many desirable properties. This paper proves that the n-dimensional alternating group graph is panyclic with a specific disjoint-cycle-cover property for n >= 4.