Cayley graph is a graph constructed out of a group Γ and a generating set A ⊆ Γ. When Γ = Zn, the corresponding Cayley graph is called as a circulant graph and denoted by Cir(n, A). In this paper, we attempt to find the total domination number of Cir(n, A) for a particular generating set A of Zn and a minimum total dominating set of Cir(n, A). Further, it is proved that Cir(n, A) is 2-total exc...

A bi-Cayley graph is a graph which admits a semiregular group of automorphisms with two orbits (of equal size), and is a onematching bi-Cayley graph if the bipartite graph induced by the edges joining these two orbits is a perfect matching. Typical examples of such graphs are the generalized Petersen graphs. A classification of connected arc-transitive one-matching bi-Cayley graphs over abelian...

A t − (n, k, ) design is a k-uniform hypergraph with the property that every set of t vertices is contained in exactly of the edges (blocks). A partial t − (n, k, ) design is a k-uniform hypergraph with the property that every set of t vertices is contained in at most edges; or equivalently the intersection of every set of + 1 blocks contains fewer than t elements. Let us denote by f (n, k, t) ...

Let S be a set of transpositions generating the symmetric group Sn (n ≥ 5). The transposition graph of S is defined to be the graph with vertex set {1, . . . , n}, and with vertices i and j being adjacent in T (S) whenever (i, j) ∈ S. In the present note, it is proved that two transposition graphs are isomorphic if and only if the corresponding two Cayley graphs are isomorphic. It is also prove...

Let G be a finite group. A subset S of G not the identity element 1 of G called C I -subset (C( stands for isomorphism"), if for any isomorphism D(G, S) ~ D(G, T), there is f AutG such that T = f(S). G is called a DCI-group if every subset of G {I} is a CI-subset. G is called a GCl-group or simply a C I -group if every inverse-closed subset of G {I} is a CI-subset. (DCI and GCl stands for "digr...

Context-free hypergraph grammars and boundary graph grammars of bounded nonterminal degree have the same power, both for generating sets of graphs and for generating sets of hypergraphs. Arbitrary boundary graph grammars have more graph generating power than context-free hypergraph grammars, but they have the same hypergraph generating power. To obtain these results, several normal forms for bo...

A colouring of the vertices of a hypergraph G is called strong if, for every edge A, the colours of all vertices in A are distinct. It corresponds to a colouring of the generated graph 0(G) obtained from G by replacing every edge by a clique. We estimate the minimum number of edges possible in a k-critical t-uniform hypergraph with a given number of vertices. In particular we show that, for k ≥...

Classification learning problem on hypergraph is an extension of multi-label classification problem on normal graph, which divides vertices on hypergraph into several classes. In this paper, we focus on the semi-supervised learning framework, and give theoretic analysis for spectral based hypergraph vertex classification semi-supervised learning algorithm. The generalization bound for such algo...

In this paper, the composite order Cayley graph Cay(G, S) is introduced, where G is a group and S is the set of all composite order elements of G. Some graph parameters such as diameter, girth, clique number, independence number, vertex chromatic number and domination number are calculated for the composite order Cayley graph of some certain groups. Moreover, the planarity of composite order Ca...