A class of orthogonal latin square graphs
نویسنده
چکیده
An orthogonal latin square graph is a graph whose vertices are latin squares of the same order, adjacency being synonymous with orthogonality. We are interested in orthogonal latin square graphs in which each square is orthogonal to the Cayley table M of a group G and is obtained from M by permuting columns. These permutations, regarded as permutations of G, are orthomorphisms of G and the graphs so obtained are orthomorphism graphs. We will discuss the main problems in the study of orthomorphism graphs and survey bounds on the clique numbers of these graphs. We will also present several problems.
منابع مشابه
A generalisation of t-designs
This paper defines a class of designs which generalise t-designs, resolvable designs, and orthogonal arrays. For the parameters t = 2, k = 3 and λ = 1, the designs in the class consist of Steiner triple systems, Latin squares, and 1-factorisations of complete graphs. For other values of t and k, we obtain t-designs, Kirkman systems, large sets of Steiner triple systems, sets of mutually orthogo...
متن کاملAtomic Latin Squares of Order Eleven
A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i 61⁄4 j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, in...
متن کاملUsing Latin Squares to Color Split Graphs
An edge-coloring of a graph is an assignment of colors to its edges such that no adjacent edges have the same color. A split graph is a graph whose vertex set admits a partition into a stable set and a clique. Split graphs have been introduced by Földes and Hammer [4] and it is a well-studied class of graphs. However, the problem of deciding the chromatic index of any split graph remains unsolv...
متن کاملOn the existence of self-orthogonal diagonal Latin squares
A diagonal Latin square is a Latin square whose main diagonal and back diagonal are both transversals. A Latin square is self-orthogonal if it is orthogonal to its transpose. In an earlier paper Danhof, Phillips and Wallis considered the question of the existence of self-orthogonal diagonal Latin squares of order 10. In this paper we shall present some constructions of self-orthogonal diagonal ...
متن کاملOrientable Hamilton Cycle Embeddings of Complete Tripartite Graphs I: Latin Square Constructions
Abstract. In an earlier paper the authors constructed a hamilton cycle embedding of Kn,n,n in a nonorientable surface for all n ≥ 1 and then used these embeddings to determine the genus of some large families of graphs. In this two-part series, we extend those results to orientable surfaces for all n 6= 2. In part I, we explore a connection between orthogonal latin squares and embeddings. A pro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 57 شماره
صفحات -
تاریخ انتشار 2013