https://novaprd-lb.newcastle.edu.au/vital/access/manager/Index ${session.getAttribute("locale")} 5 Vertex-magic labelings of regular graphs II https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:7865 Wed 24 Jul 2013 22:43:09 AEST ]]> Square-free rank of integers https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:41366 3a2 2 > · · · > pka2 k with pi(ai + 1)2 > 2a21for 1 < i < k, and the corresponding sequences in which all the inequalities are reversed and {equation presented}. We show that (3n2 | n ∈ N) has no member in the interval [2a2,2(a+ 1)2] with a ∈ N if and only if a is in the Beatty sequence ([n (3 + √6)] | n ∈ N); several generalisations are studied. Finally, we study closest linear combinations {equation presented}.]]> Wed 17 Aug 2022 15:35:48 AEST ]]> Vertex-magic labelings: mutations https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:7777 Wed 11 Apr 2018 17:19:24 AEST ]]> All regular graphs of small odd order are vertex-magic https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:9139 Wed 11 Apr 2018 17:07:23 AEST ]]> Rational and Heron tetrahedra https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:1082 Wed 11 Apr 2018 15:49:02 AEST ]]> Sparse anti-magic squares and vertex-magic labelings of bipartite graphs https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:6466 Wed 11 Apr 2018 14:50:17 AEST ]]> Rational tetrahedra with edges in geometric progression https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:4995 Wed 11 Apr 2018 14:45:34 AEST ]]> Principal rank plateaux in the integers beyond 10¹² https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:4278 Wed 11 Apr 2018 14:38:38 AEST ]]> Heron quadrilaterals with sides in arithmetic or geometric progression https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:6511 Wed 11 Apr 2018 13:10:12 AEST ]]> Consecutive integers with equally many principal divisors https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:5577 Wed 11 Apr 2018 12:24:20 AEST ]]> Strong VMTLs of odd order 2-regular graphs https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:7667 Wed 11 Apr 2018 12:11:03 AEST ]]> Runs of integers with equally many distinct prime factors https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:11712 Wed 11 Apr 2018 12:05:04 AEST ]]> Principal divisor ranks of the first trillion positive integers https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:4185 Wed 11 Apr 2018 11:37:33 AEST ]]> Strong edge-magic graphs of maximum size https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:4997 Wed 11 Apr 2018 10:44:45 AEST ]]> Minimally triangle-saturated graphs: adjoining a single vertex https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:1417 Wed 11 Apr 2018 10:33:55 AEST ]]> Structure of graph posets for orders 4 to 8 https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:1699 Sat 24 Mar 2018 11:11:14 AEDT ]]> Graphs with a given degree sequence https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:6510 Sat 24 Mar 2018 11:04:30 AEDT ]]> Degree sequences and poset structure of order 9 graphs https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:6509 Sat 24 Mar 2018 11:04:30 AEDT ]]> Taxonomy of graphs of order 10 https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:6508 Sat 24 Mar 2018 11:04:30 AEDT ]]> Rational tetrahedra with edges in arithmetic progression https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:122 Sat 24 Mar 2018 11:03:15 AEDT ]]> The maximum dimension of a subspace of nilpotent matrices of index 2 https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:7996 n and suppose that r is the maximum rank of any matrix in V. The object of this paper is to give an elementary proof of the fact that dim V ≤ r(n − r). We show that the inequality is sharp and construct all such subspaces of maximum dimension. We use the result to find the maximum dimension of spaces of anti-commuting matrices and zero subalgebras of special Jordan Algebras.]]> Sat 24 Mar 2018 08:42:37 AEDT ]]> Graphs which are linked cycles https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:7966 Sat 24 Mar 2018 08:40:09 AEDT ]]> Graphs which are linked structures https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:7962 2, and many with an automorphism of order n = 2, are in fact n-linked cycles, and this viewpoint leads to a "generalized factorization" of such graphs.]]> Sat 24 Mar 2018 08:40:08 AEDT ]]> Sparse semi-magic squares and vertex-magic labelings https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:1158 Sat 24 Mar 2018 08:28:43 AEDT ]]> Cyclic polygons with rational sides and area https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:4922 Sat 24 Mar 2018 07:21:12 AEDT ]]>