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**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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**Date:** 2011
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/920376
**Description:** This paper deals with vertex-magic total labellings of graphs. Earlier work by many authors has shown many infinite families of graphs to admit such labelings. The fact that many of these graphs are r... More
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**Date:** 2011
**Keyword:** strong vertex magic total labellings | even regular odd degree graphs | Gray's construction
**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:** 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
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**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
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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:** 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
**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
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**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
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**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
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**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
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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
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**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:** 2008
**Resource Type:** journal article
**Identifier:** uon:4997
**Description:** An edge-magic total labeling on G is a one-to-one map λ from V(G)∪E(G) onto the integers 1,2,...,|V(G)∪E(G)| with the property that, given any edge (x,y), λ(x)+λ(x,y)+λ(y)=k for some constant k. The l... 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
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