In this paper we apply Pólya’s Theorem to the problem of enumerating Cayley graphs on permutation groups up to isomorphisms induced by conjugacy in the symmetric group. We report the results of a search of all three-regular Cayley graphs on permutation groups of degree at most nine for small diameter graphs. We explore several methods of constructing covering graphs of these Cayley graphs. Exam...

Tissue engineering, using either polymer or biological based scaffolds, represents the newest approach to overcoming limitations of small diameter prosthetic vascular grafts. Their disadvantages include thromboembolism and thrombosis, anticoagulant related haemorrhage, compliance mismatch, neointimal hyperplasia, as well as aneurysm formation. This current review represents an overview about pr...

We investigate decompositions of a graph into a small number of low diameter subgraphs. Let P (n, 2, d) be the smallest k such that every graph G = (V, E) on n vertices has an edge partition E = E0 ∪ E1 ∪ . . . ∪ Ek such that |E0| ≤ 2n and for all 1 ≤ i ≤ k the diameter of the subgraph spanned by Ei is at most d. Using Szemerédi’s regularity lemma, Polcyn and Ruciński showed that P (n, 2, 4) is...

A graph is superconnected, for short super-κ, if all minimum vertex-cuts consist of the vertices adjacent with one vertex. In this paper we prove for any r-regular graph of diameter D and odd girth g that if D ≤ g − 2, then the graph is super-κ when g ≥ 5 and a complete graph otherwise.

BACKGROUND/AIMS The clinical definition of an atypical naevus ("dysplastic naevus" or "naevus with architectural disorder and cytological atypia of melanocytes") stresses size larger than 5 mm in diameter as a major diagnostic criterion. Because malignant melanomas and their precursors may arise in smaller lesions, a histological study of melanocytic lesions smaller than 4 mm in diameter was co...

Introduction: Crater counting has historically been used to establish relative and absolute chronologies on planetary surfaces and to develop global stratigraphies. Typically, craters in the size range >1 km have been used. This diameter was chosen as a convenient balance between image resolution and a diameter that would indicate a formation age. Craters at larger diameters might be craters pr...

k) denote the l1um ber of of order nand diam-In this paper it is that: fixed k :~, ii) for every fixed k 1, n! where with D(n;d=n k:):Sn! (n) are polynomials of degree k 1 in n coefficients depending only on k. c;o:rres1)(:m(img results for undirected graphs given in [2]. of a vertex :r is the number of vertices of CJ that nr1PO'l'PP d-(x) is the number of vertices of G ~UII~~'~HU connected dig...

In this research, biodiversity was investigated in the species diversity level. The objective of this research was to study of Norway Maple (Acer platanoides L.) dispersion and biodiversity of associated woody species in the Shafaroud forests, Gilan (IRAN). In this regard, a 0.5 ha lozenge sample plot was selected with considering presence of Norway Maple in each site. In each plot, geographic ...