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Representations of graphs and orthogonal latin square graphs

✍ Scribed by Paul Erdös; Anthony B. Evans

Publisher
John Wiley and Sons
Year
1989
Tongue
English
Weight
155 KB
Volume
13
Category
Article
ISSN
0364-9024

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📜 SIMILAR VOLUMES

Orthogonal latin square graphs
Orthogonal latin square graphs
✍ Charles C. Lindner; E. Mendelsohn; N. S. Mendelsohn; Barry Wolk 📂 Article 📅 1979 🏛 John Wiley and Sons 🌐 English ⚖ 617 KB

## Abstract An orthogonal latin square graph (OLSG) is one in which the vertices are latin squares of the same order and on the same symbols, and two vertices are adjacent if and only if the latin squares are orthogonal. If __G__ is an arbitrary finite graph, we say that __G__ is realizable as an O

Automorphism free latin square graphs
Automorphism free latin square graphs
✍ K.T. Phelps 📂 Article 📅 1980 🏛 Elsevier Science 🌐 English ⚖ 837 KB

In this paper, we show that there exists an automorphism free latin square graph of order n for all n a 7 and that the number of such graphs goes to infinity with n. These results are then applied to the construction of automorphism free Steiner triple systems.

Mutually orthogonal graph squares
Mutually orthogonal graph squares
✍ R. Sampathkumar; S. Srinivasan 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 89 KB

## Abstract A __decomposition__ 𝒢={__G__~1~, __G__~2~,…,__G__~__s__~} of a graph G is a partition of the edge set of G into edge‐disjoint subgraphs __G__~1~, __G__~2~,…,__G__~__s__~. If __G__~__i__~≅__H__ for all __i__∈{1, 2, …, __s__}, then 𝒢 is a decomposition of G by H. Two decompositions 𝒢={__G

Embedding a latin square in a pair of or
Embedding a latin square in a pair of orthogonal latin squares
✍ Peter Jenkins 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 123 KB

## Abstract In this paper, it is shown that a latin square of order __n__ with __n__ ≥ 3 and __n__ ≠ 6 can be embedded in a latin square of order __n__^2^ which has an orthogonal mate. A similar result for idempotent latin squares is also presented. © 2005 Wiley Periodicals, Inc. J Combin Designs 1

Orthogonal factorizations of graphs
Orthogonal factorizations of graphs
✍ Haodi Feng; Guizhen Liu 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 92 KB

## Abstract Let __G__ be a graph with vertex set __V__(__G__) and edge set __E__(__G__). Let __k__~1~, __k__~2~,…,__k__~m~ be positive integers. It is proved in this study that every [0,__k__~1~+…+__k__~__m__~−__m__+1]‐graph __G__ has a [0, __k__~i~]~1~^__m__^‐factorization orthogonal to any given