GlobalView

Showing items 1 - 15 of 24.

Add to Quick Collection   All 24 Results

Sort:
 Add All Items to Quick Collection
Date: 2004
Keyword: graph posets
Resource Type: journal article
Identifier: uon:1699
Description: The poset G(n) comprises the unlabelled simple graphs of order n, with partial ordering G ≤ H whenever G is a spanning subgraph of H. We define a modified Steinbach numbering of the graphs in G(n), ap... More
Reviewed: Reviewed
Image Thumbnail
Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/916345
Description: A graph H of order h is an n-linked cycle if it has an induced subgraph G of order g < h and an automorphism α: H → H of order n ≥ 2 such that H = ⋃{αr(G) : 0 ≤ r < n} and G has an induced subgraph K ... More
Reviewed: Reviewed
Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/808876
Description: In this paper, we are studying vertex-magic total labelings of simple graphs. We introduce a procedure called mutation which transforms one labeling into another by swapping sets of edges among vertic... More
Full Text: Full Text
Reviewed: Reviewed
Image Thumbnail
Date: 2009
Resource Type: journal article
Identifier: uon:7996
Description: A matrix M is nilpotent of index 2 if M² = 0. Let V be a space of nilpotent n x n matrices of index 2 over a field k where card k > n and suppose that r is the maximum rank of any matrix in V. The obj... More
Reviewed: Reviewed
Date: 2006
Keyword: 05C99 | 05C07 | 06A07
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/803795
Description: Extending earlier data summaries for graphs of order n ≤ 9, this paper describes structural characteristics and relationships for the 12005168 graphs of order 10. It summarises data for their degree s... More
Reviewed: Reviewed
Date: 2008
Resource Type: journal article
Identifier: uon:5577
Description: The Fundamental Theorem of Arithmetic is usually stated in a form emphasizing how primes enter the structure of the positive integers, such as: Every positive integer is the product of a unique finite... More
Full Text: Full Text
Reviewed: Reviewed
Image Thumbnail
Date: 2009
Language: eng
Resource Type: report
Identifier: http://hdl.handle.net/1959.13/38076
Description: A Chinese Remainder method is developed for determining likely positive integers n starting maximal runs of size s and constant principal rank r, that is, {n + i ∈ ℤ⁺, 0 ≤ i < s : ω(n + i) = r} with ω... More
Full Text: Full Text
Image Thumbnail
Date: 2009
Language: eng
Resource Type: report
Identifier: http://hdl.handle.net/1959.13/35886
Description: The principal divisors of a positive integer n are its maximal prime-power divisors. The principal divisor rank ω(n) is the number of such divisors, also equal to the number of distinct prime divisors... More
Full Text: Full Text
Image Thumbnail
Date: 2005
Language: eng
Resource Type: journal article
Identifier: uon:122
Description: This paper discusses tetrahedra with rational edges forming an arithmetic progression, focussing specifically on whether they can have rational volume or rational face areas. Several infinite families... More
Reviewed: Reviewed
Date: 2006
Resource Type: journal article
Identifier: uon:1082
Description: Buchholz [R.H. Buchholz, Perfect pyramids, Bull. Austral. Math. Soc. 45 (1991) 353–368] began a systematic search for tetrahedra having integer edges and volume by restricting his attention to those w... More
Full Text: Full Text
Reviewed: Reviewed
Image Thumbnail
Date: 2008
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/42850
Description: This paper discusses tetrahedra with rational edges forming a geometric progression, focussing on whether they can have rational volume or rational face areas. We examine the 30 possible configuration... More
Full Text: Full Text
Reviewed: Reviewed
Image Thumbnail
Date: 2009
Keyword: magic labeling
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/915980
Description: Previously the first author has shown how to construct vertex-magic total labelings (VMTLs) for large families of regular graphs. The construction proceeds by successively adding arbitrary 2-factors t... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/933758
Description: We survey and update data on runs of consecutive integers each having exactly r distinct prime factors (briefly, of principal rank r). For 3 ≤ r ≤ 64 and other sporadic values, lower bounds are given ... More
Full Text: Full Text
Reviewed: Reviewed
Image Thumbnail
Date: 2006
Language: eng
Resource Type: journal article
Identifier: uon:6510
Description: The level set G(n,m) comprises all unlabelled simple graphs of order n and size m, and is partitioned into similarity classes, comprising all graphs with the same degree sequence. When graphs are orde... More
Reviewed: Reviewed
Date: 1999
Language: eng
Resource Type: journal article
Identifier: uon:6511
Description: We study triangles and cyclic quadrilaterals which have rational area and whose sides form geometric or arithmetic progressions. A complete characterization is given for the infinite family of triangl... More
Full Text: Full Text
Reviewed: Reviewed
Image Thumbnail