316 research outputs found
Classification and Galois conjugacy of Hamming maps
We show that for each d>0 the d-dimensional Hamming graph H(d,q) has an
orientably regular surface embedding if and only if q is a prime power p^e. If
q>2 there are up to isomorphism \phi(q-1)/e such maps, all constructed as
Cayley maps for a d-dimensional vector space over the field of order q. We show
that for each such pair d, q the corresponding Belyi pairs are conjugate under
the action of the absolute Galois group, and we determine their minimal field
of definition. We also classify the orientably regular embedding of merged
Hamming graphs for q>3
Spectra and the exact number of Automorphisms of Paley-type graphs of order a product of n distinct primes
Paley graphs are Cayley graphs which are circulant and strongly regular.
Paley-type graph of order a product of two distinct Pythagorean primes was
introduced by Dr Angsuman Das. In this paper, we extend the study of Paley-type
graphs to the order a product of n distinct Pythagorean primes. We have
determined its adjacency spectra and the exact number of the automorphisms
Brick assignments and homogeneously almost self-complementary graphs
AbstractA graph is called almost self-complementary if it is isomorphic to the graph obtained from its complement by removing a 1-factor. In this paper, we study a special class of vertex-transitive almost self-complementary graphs called homogeneously almost self-complementary. These graphs occur as factors of symmetric index-2 homogeneous factorizations of the “cocktail party graphs” K2n−nK2. We construct several infinite families of homogeneously almost self-complementary graphs, study their structure, and prove several classification results, including the characterization of all integers n of the form n=pr and n=2p with p prime for which there exists a homogeneously almost self-complementary graph on 2n vertices
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