recently, hua et al. defined a new topological index based on degrees and inverse ofdistances between all pairs of vertices. they named this new graph invariant as reciprocaldegree distance as 1{ , } ( ) ( ( ) ( ))[ ( , )]rdd(g) = u v v g d u  d v d u v , where the d(u,v) denotesthe distance between vertices u and v. in this paper, we compute this topological index forgrassmann graphs.

The minimal degree of an inverse semigroup S is the minimal cardinality of a set A such that S is isomorphic to an inverse semigroup of one-to-one partial transformations of A . The main result is a formula that expresses the minimal degree of a finite inverse semigroup S in terms of certain subgroups and the ordered structure of S . In fact, a representation of S by one-to-one partial transfor...

A semilattice decomposition of an inverse semigroup has good internal mapping properties. These are used to give natural proofs of some embedding theorems, which were originally proved in a rather artificial way. The reader is referred to [1] for the basic theory of inverse semigroups. In an earlier paper [3] we proved the following embedding result: (1) An E-unitary inverse semigroup is isomor...

In this article, we study the Bergman property for semigroups and the associated notions of cofinality and strong cofinality. A large part of the paper is devoted to determining when the Bergman property, and the values of the cofinality and strong cofinality, can be passed from semigroups to subsemigroups and vice versa. Numerous examples, including many important semigroups from the literatur...

We study the receptive metric entropy for semigroup actions on probability spaces, inspired by a similar notion of topological introduced Hofmann and Stoyanov. analyze its basic properties relation with classical entropy. In case compact spaces we compare looking Variational Principle. With this aim propose several characterizations Finally introduce local Bowen generalized in setting amenable ...

We study C*-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C*algebras as C*-algebras of inverse semigroups, groupoid C*-algebras and full corners in associated group crossed products. These descriptions allow us to characterize nuclear...