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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/1959.13/808876
**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:** 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
**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:** 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:** 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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**Date:** 1999
**Keyword:** number theory | 51M04 | 11D25 | diophantine equations | cubic and quartic equations | elementary problems in Euclidean geometries
**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:** 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:** 2002
**Keyword:** triangle-saturated graphs | primitive minimally saturated extensions | triangle-free graphs | vertex addition
**Resource Type:** journal article
**Identifier:** uon:1417
**Description:** A graph G is triangle-saturated if every possible edge addition to G creates one or more new triangles (3-cycles). Such a graph is minimally triangle-saturated if removal of any edge from G leaves a g... 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:** 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
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**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:** 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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