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