A graph is called almost self-complementary if it is isomorphic to one of its almost complements Xc − I, where Xc denotes the complement of X and I a perfect matching (1-factor) in Xc. Almost self-complementary circulant graphs were first studied by Dobson and Šajna in 2004. In this paper we investigate some of the properties and constructions of general almost self-complementary graphs. In par...

The tensor product, also called direct, categorical, or Kronecker product of graphs, is one of the least-understood graph products. In this paper we determine partial answers to the question given in the title, thereby significantly extending results of Broere and Hattingh (see [2]). We characterize completely those pairs of complete graphs whose tensor products are circulant. We establish that...

A description is given of finite permutation groups containing a cyclic regular subgroup. It is then applied to derive a classification of arc transitive circulants, completing the work dating from 1970’s. It is shown that a connected arc transitive circulant of order n is one of the following: a complete graph Kn , a lexicographic product [K̄b], a deleted lexicographic product [K̄b] − b , where ...

We characterize the automorphism groups of circulant digraphs whose connection sets are relatively small, and of unit circulant digraphs. For each class, we either explicitly determine the automorphism group or we show that the graph is a “normal” circulant, so the automorphism group is contained in the normalizer of a cycle. Then we use these characterizations to prove results on the automorph...

This paper explores dense Gaussian Networks, which are interconnection networks based on dense Circulant graphs of degree four. Gaussian networks exhibit better distance related characteristics than equivalent topologies such as Tori. We will show that the Gaussian integers, or the set of complex numbers with integer coefficients, constitute the appropriate mathematical model to deal with these...

A graph X is k-arc-transitive if its automorphism group acts transitively on the set of it-arcs of X. A circulant is a Cayley graph of a cyclic group. A classification of 2-arc-transitive circulants is given.

In this paper, we extend the notion of a circulant to a broader class of vertex.transitive graphs, which we call multidimensional circulants. This new class of graphs is shown to consist precisely of those vertextransitive graphs with an automorphism group containing a regular abelian subgroup. The result is proved using a theorem of Sabidussi which shows how to recover any vertex-transitive gr...

for a graph $g$ let $gamma (g)$ be its domination number. we define a graph g to be (i) a hypo-efficient domination graph (or a hypo-$mathcal{ed}$ graph) if $g$ has no efficient dominating set (eds) but every graph formed by removing a single vertex from $g$ has at least one eds, and (ii) a hypo-unique domination graph (a hypo-$mathcal{ud}$ graph) if $g$ has at least two minimum dominating sets...

A perfect code in a graph Γ = (V,E) is a subset C of V that is an independent set such that every vertex in V \ C is adjacent to exactly one vertex in C. A total perfect code in Γ is a subset C of V such that every vertex of V is adjacent to exactly one vertex in C. A perfect code in the Hamming graph H(n, q) agrees with a q-ary perfect 1-code of length n in the classical setting. A necessary a...

Graph-Structured Data Viewed Through a Fourier Lens by Venkatesan Nallampatti Ekambaram Doctor of Philosophy in Electrical Engineering and Computer Science University of California, Berkeley Professor Kannan Ramchandran, Chair Graph-structured data appears in many modern applications like social networks, sensor networks, transportation networks and computer graphics. These applications are def...