Author:
Fish Washiela,Fray Roland,Mwambene Eric
Abstract
AbstractFor k ≥ 1, the odd graph denoted by O(k), is the graph with the vertex-set Ω{k}, the set of all k-subsets of Ω = {1, 2, …, 2k +1}, and any two of its vertices u and v constitute an edge [u, v] if and only if u ∩ v = /0. In this paper the binary code generated by the adjacency matrix of O(k) is studied. The automorphism group of the code is determined, and by identifying a suitable information set, a 2-PD-set of the order of k 4 is determined. Lastly, the relationship between the dual code from O(k) and the code from its graph-theoretical complement $\overline {O(k)} $, is investigated.
Reference11 articles.
1. Bailey R.F., Distance-Transitive Graphs, MMath thesis, University of Leeds, 2002
2. Balaban A.T., Chemical graphs, part XII: Combinatorial patterns, Rev. Roumaine Math. Pures Appl., 1972, 17, 3–16
3. Ball R.W., Maximal subgroups of symmetric groups, Trans. Amer. Math. Soc., 1966, 121(2), 393–407
4. Biggs N., An edge-colouring problem, Amer. Math. Monthly, 1972, 79(9), 1018–1020
5. Cameron P.J., Automorphism groups of graphs, In: Selected Topics in Graph Theory, 2, Academic Press, London, 1983, 89–127
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献