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Date: 2011
Language: eng
Resource Type: report
Identifier: uon:7667
Description: Tables of edge cycles proving the theorem: Other than the three graphs, $C_{3} cup C_{4}$, $2C_{3} cup C_{5}$ and $3C_{3} cup C_{4}$, every 2-regular graph of odd order less than 30 has a strong verte... More
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Date: 2008
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/41712
Description: We generalise the notion of Heron triangles to rational-sided, cyclic n-gons with rational area using Brahmagupta's formula for the area of a cyclic quadrilateral and Robbins' formulæ for the area of ... More
Reviewed: Reviewed
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: 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
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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: 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
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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
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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
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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
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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/1959.13/916332
Description: A linked pair is a graph H = G₀ ⋃ G₁ formed from (1) a given finite graph G,(2) isomorphic induced proper subgraphs K and K*, not necessarily distinct, and (3) a graph isomorphism σ: K* → K. The graph... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: uon:6466
Description: A sparse anti-magic square is an n X n array whose non-zero entries are the consecutive integers 1,...,m for some m ≤ n² and whose row-sums and column-sums form a set of consecutive integers: We deriv... More
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Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/26848
Description: We introduce a generalisation of the traditional magic square which proves useful in the construction of magic labelings of graphs. An order n sparse semi-magic square is an x n array containing the e... More
Reviewed: Reviewed
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
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