Connectivity of generalized prisms over G

Small Covers over Prisms

In this paper we calculate the number of equivariant diffeomorphism classes of small covers over a prism.

Hamiltonian decompositions of prisms over cubic graphs

Expanding generalized Hadamard matrices over Gm by substituting several generalized Hadamard matrices over G

Over an additive abelian group of order and for a given positive integer , a generalized Hadamard matrix is defined as a matrix , where and , such that every element of appears exactly times in the list , , , , for any . In this paper, we propose a new method of expanding a over by replacing each of its -tuple with where . We may use (not necessarily all distinct) ’s for the substitution and th...

Hamilton cycles in prisms over graphs

The prism over a graph G is the Cartesian product G2K2 of G with the complete graph K2. If G is hamiltonian, then G2K2 is also hamiltonian but the converse does not hold in general. Having a hamiltonian prism is shown to be a good measure how close a graph is to being hamiltonian. In this paper, we examine classical problems on hamiltonicity of graphs in the context of hamiltonian prisms.

On generalized atom-bond connectivity index of cacti

The generalized atom-bond connectivity index of a graph G is denoted by ABCa(G) and defined as the sum of weights ((d(u)+d(v)-2)/d(u)d(v))aa$ over all edges uv∊G. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, we compute sharp bounds for  ABCa index for cacti of order $n$ ...