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Harary Index of Product Graphs

100%

Pattabiraman K. , Paulraja P.

tom 35

nr 1

17-33

The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, the exact formulae for the Harary indices of tensor product G × Km0,m1,...,mr−1 and the strong product G⊠Km0,m1,...,mr−1 , where Km0,m1,...,mr−1 is the complete multipartite graph with partite sets of sizes m0,m1, . . . ,mr−1 are obtained. Also upper bounds for the Harary indices of tensor and strong products of graphs are estabilished. Finally, the exact formula for the Harary index of the wreath product G ○ G′ is obtained.

Semigroup of Contractions of Wreath Products of Metric Spaces

100%

Oliynyk B.

Discussiones Mathematicae - General Algebra and Applications

2010

tom 30

nr 1

35-43

In this paper semigroups of contractions of metric spaces are considered. The semigroup of contractions of the wreath product of metric spaces is calculated.

The Krohn-Rhodes Theorem and Local Divisors

88%

Diekert V. , Kufleitner M. , Steinberg B.

2012

tom Vol. 116, nr 1-4

65-77

We give a new proof of the Krohn-Rhodes theorem using local divisors. The proof provides nearly as good a decomposition in terms of size as the holonomy decomposition of Eilenberg, avoids induction on the size of the state set, and works exclusively with monoids with the base case of the induction being that of a group.

Involutive bases of Sylow 2-subgroups of symmetric and alternating groups

75%

Pawlik B.

Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska

2015

tom z. 5

35--42

The paper presents a construction of Sylow 2-subgroups of symmetric and alternating groups, which bases contains only an involutions. Polynomial representation of Sylow 2-subgroups was used.

W artykule przedstawiono konstrukcję takich 2-podgrup Sylowa grup symetrycznych i alternujących, których bazy zawierają wyłącznie inwolucje. Zastosowano reprezentację 2-podgrup Sylowa za pomocą zredukowanych wielomianów wielu zmiennych nad ciałem Z2.

Wreath product of a semigroup and a Γ-semigroup

63%

Sen M. , Chattopadhyay S.

Discussiones Mathematicae - General Algebra and Applications

2008

tom 28

nr 2

161-178

Let S = {a,b,c,...} and Γ = {α,β,γ,...} be two nonempty sets. S is called a Γ -semigroup if aαb ∈ S, for all α ∈ Γ and a,b ∈ S and (aαb)βc = aα(bβc), for all a,b,c ∈ S and for all α,β ∈ Γ. In this paper we study the semidirect product of a semigroup and a Γ-semigroup. We also introduce the notion of wreath product of a semigroup and a Γ-semigroup and investigate some interesting properties of this product.