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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
Reviewed: Reviewed
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
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: 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: 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
Reviewed: Reviewed
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: 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
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
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
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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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