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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: 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: 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: 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: 2002
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: 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: 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: 2004
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/803792
Description: The set G(n) of unlabelled simple graphs of order n is a poset with partial ordering G ≤ H whenever G is a spanning subgraph of H. On the website www.maths.uq.edu.au/~pa/research/poset9.html we have m... More
Reviewed: Reviewed
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: 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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