Equitable partitions of Latin-square graphs
نویسندگان
چکیده
منابع مشابه
Unique square property, equitable partitions, and product-like graphs
Equivalence relations on the edge set of a graph G that satisfy restrictive conditions on chordless squares play a crucial role in the theory of Cartesian graph products and graph bundles. We show here that such relations in a natural way induce equitable partitions on the vertex set of G, which in turn give rise to quotient graphs that can have a rich product structure even if G itself is prime.
متن کاملRandom Latin square graphs
In this paper we introduce new models of random graphs, arising from Latin squares which include random Cayley graphs as a special case. We investigate some properties of these graphs including their clique, independence and chromatic numbers, their expansion properties as well as their connectivity and Hamiltonicity. The results obtained are compared with other models of random graphs and seve...
متن کاملk-Efficient partitions of graphs
A set $S = {u_1,u_2, ldots, u_t}$ of vertices of $G$ is an efficientdominating set if every vertex of $G$ is dominated exactly once by thevertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$%, we note that ${U_1, U_2, ldots U_t}$ is a partition of the vertex setof $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices atdistance~1 from it in $G$. In this ...
متن کاملEquitable Partitions and Orbit Partitions
We consider two kinds of partition of a graph, namely orbit partitions and equitable partitions. Although an orbit partition is always an equitable partition, the converse is not true in general. We look at some classes of graphs for which the converse is true.
متن کاملOn chromatic number of Latin square graphs
The chromatic number of a Latin square is the least number of partial transversals which cover its cells. This is just the chromatic number of its associated Latin square graph. Although Latin square graphs have been widely studied as strongly regular graphs, their chromatic numbers appear to be unexplored. We determine the chromatic number of a circulant Latin square, and find bounds for some ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Designs
سال: 2018
ISSN: 1063-8539
DOI: 10.1002/jcd.21634