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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:** 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:** 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:** 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
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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
**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:** 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
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**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
**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
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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:** 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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