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Miller, Mirka

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Date: 2013
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/44102
Description: We consider the bipartite version of the degree/diameter problem, namely, given natural numbers d≥2 and D≥2, find the maximum number N b(d,D) of vertices in a bipartite graph of maximum degree d a... More
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Date: 2011
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/58296
Description: In this paper we consider the degree/diameter problem, namely, given natural numbers Δ<2 and D<1, find the maximum number N(Δ,D) of vertices in a graph of maximum degree Δ and diameter D. In this c... More
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Date: 2011
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/56686
Description: An (a, d)-edge-antimagic total labeling on (p, q)-graph G is a one-to-one map f from V(G) ∪ E(G) onto the integers 1,2,...,p + q with the property that the edge-weights, w(uv) = f(u)+f(v)+f(uv) where ... More
Reviewed: Reviewed
Date: 2009
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/39316
Description: A graph G is called (a, d)-edge-antimagic total if it admits a labeling of the vertices and edges by pairwise distinct integers of 1,2,..., |V(G)| + |E(G)| such that the edge-weights, w(uÏ…) = f(u) + ... More
Reviewed: Reviewed
Date: 2009
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/44848
Description: We consider graphs of maximum degree 3, diameter D≥2 and at most 4 vertices less than the Moore bound M3,D, that is, (3,D,−)-graphs for ≤4. We prove the non-existence of (3,D,−4)-graphs for D≥5, compl... More
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Date: 2009
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/33760
Description: In the pursuit of obtaining largest graphs of given maximum degree
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Date: 2009
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/32353
Description: It is known that the Moore bipartite bound provides an upper bound on the order of a connected bipartite graph. In this paper we deal with bipartite graphs of maximum degree
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Date: 2009
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/41411
Description: We consider bipartite graphs of degree A<2, diameter D = 3, and defect 2 (having 2 vertices less than the bipartite Moore bound). Such graphs are called bipartite (â–³,3, -2) -graphs. We prove the uni... More
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Date: 2009
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/63442
Description: In 1960, Hoffman and Singleton investigated the existence of Moore graphs of diameter 2 (graphs of maximum degree d and d² + 1 vertices), and found that such graphs exist only for d = 2; 3; 7 and poss... More
Reviewed: Reviewed
Date: 2008
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/54112
Reviewed: Reviewed
Date: 2008
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/70067
Description: An almost Moore digraph G of degree d > 1, diameter k > 1 is a diregular digraph with the number of vertices one less than the Moore bound. If G is an almost Moore digraph, then for each vertex u ∈ V ... More
Reviewed: Reviewed
Date: 2008
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/39135
Description: The Moore bound for a directed graph of maximum out-degree d and diameter k is Md,k=1+d+d2++dk. It is known that digraphs of order Md,k (Moore digraphs) do not exist for d>1 and k>1. Similarly, the Mo... More
Reviewed: Reviewed
Date: 2008
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/63608
Description: The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree and given diameter. This paper deals with directed graphs. General upper bounds, called Moore bounds,... More
Reviewed: Reviewed
Date: 2008
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/56589
Description: Mixed graphs contain both undirected as well as directed links between vertices and therefore are an interesting model for interconnection communication networks. In this paper, we establish the Moore... More
Reviewed: Reviewed
Date: 2008
Type: Text
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/67727
Reviewed: Reviewed