Abstract The connectivity is an important measurement for the fault-tolerance of a network. generalized natural generalization classical connectivity. An S S -tree connected graph G G tree T = ( V ? , <m:m...

let g be a simple connected graph. the generalized polarity wiener index ofg is defined as the number of unordered pairs of vertices of g whosedistance is k. some formulas are obtained for computing the generalizedpolarity wiener index of the cartesian product and the tensor product ofgraphs in this article.

Let H be the cartesian product of a family finite abelian groups indexed by set Ω. A given poset (i.e., partially ordered set) P = (Ω, ≼P) gives rise to metric on H, which further leads partition Q(H, P) H. We prove that if is Fourier-reflexive, then its dual Λ coincides with Ĥ induced P, and moreover, necessarily hierarchical. This result establishes conjecture proposed Gluesing-Luerssen in [5...

In this paper we follow the study of the hierarchical product of graphs, an operation recently introduced in the context of networks. A well-known example of such a product is the binomial tree which is the (hierarchical) power of the complete graph on two vertices. An appealing property of this structure is that all the eigenvalues are distinct. Here we show how to obtain a graph with this pro...