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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
**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
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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
**Reviewed:**
**Date:** 2006
**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
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**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
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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:** 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:** 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
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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:** 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:** 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:** 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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