The alternating group graph is the undirected Cayley graph of the set of generators of the alternating group given by , , , , ..., , and , where
in permutation cycle notation (Jwo et al. 1993).
is a special case of the arrangement graph given by . This and other special cases are summarized in the following table and illustrated above.
is Hamiltonian (Jwo et al. 1993), and when is an integer, contains mutually independent (directed) Hamiltonian cycles (Su et al. 2012).
The independence ratios for with , 3, 4, 5, and 6 are 1, 1/3, 1/3, 1/3, and 1/3, but the value for is apparently not known (S. Wagon, pers. comm., Jul. 30, 2018).
Precomputed properties of alternating group graphs are available in the Wolfram Language as GraphData["AlternatingGroupGraph", n].
See alsoAlternating Group,
Arrangement Graph,
Cayley Graph,
Permutation Star Graph Explore with Wolfram|Alpha ReferencesJwo, J. S.; Lakshmivarahan, S.; and Dhall, S. K. "A New Class of Interconnectional Networks Based on the Alternating Group." Networks 23, 315-326, 1993.Su, H.; Chen, S.-Y.; and Kao, S.-S. "Mutually Independent Hamiltonian Cycles in Alternating Group Graphs." J. Supercomput. 61, 560-571, 2012. Referenced on Wolfram|AlphaAlternating Group Graph Cite this as:Weisstein, Eric W. "Alternating Group Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AlternatingGroupGraph.html
Subject classificationsRetroSearch is an open source project built by @garambo | Open a GitHub Issue
Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo
HTML:
3.2
| Encoding:
UTF-8
| Version:
0.7.4