The theory of hyperstructures has been introduced byMarty in 1934 during the 8th Congress of the Scandinavian Mathematicians [4]. Marty introduced the notion of a hypergroup and since then many researchers have worked on this new topic of modern algebra and developed it. The notion of a hyperfield and a hyperring was studied first by Krasner [2] and then some authors followed him, for example, ...

The vertex boundary-width problem (for short VBWP) is to determine the value of vbw(G)=max1 |V |minS⊆V,|S|= |N(S)| for a given graph G= (V ,E), where N(S)= {v / ∈ S|v is a neighbor of u for some u ∈ S}. In this paper, we give a lower bound for vertex boundary-width of complete k-ary trees. © 2007 Elsevier B.V. All rights reserved.

Following [1], in this note we compute the average number of protected points in all k-ary trees with n internal points.

we describe under various conditions abelian subgroups of the automorphism‎ ‎group $mathrm{aut}(t_{n})$ of the regular $n$-ary tree $t_{n}$‎, ‎which are‎ ‎normalized by the $n$-ary adding machine $tau =(e‎, ‎dots‎, ‎e,tau )sigma _{tau‎ ‎}$ where $sigma _{tau }$ is the $n$-cycle $left( 0,1‎, ‎dots‎, ‎n-1right) $‎. ‎as‎ ‎an application‎, ‎for $n=p$ a prime number‎, ‎and for $n=4$‎, ‎we prove that...

measure always exists on a commutative hypergroup K, and there always exists a 'Plancherel measure' on the dual space K of equivalence classes of irreducible representations of K, with respect to which Plancherel's formula holds for Fourier transforms. In contrast with the case of a locally compact abelian group, however, the Plancherel measure is not necessarily a Haar measure on K, and K need...

This paper continues the study of the connection between hyper- groups and fuzzy sets, investigating the length of the sequence of join spaces associated with a hypergroup. The classes of complete hypergroups and of 1-hypergroups are considered and analyzed in this context. Finally, we give a method to construct a nite hypergroup with the strong fuzzy grade equal to a given natural number

In this paper, we determine the expectation and variance of Xn the external path length in a random recursive k-ary tree of size n.