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**Date:** 2013
**Subject:** 0101 Pure Mathematics | 0102 Applied Mathematics | Bipartite Moore bound | Defect | Degree/diameter problem for bipartite graphs | Large bipartite graphs
**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 dâ‰¥2 and Dâ‰¥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
**Subject:** Defect | Degree/diameter problem | Moore bound | Moore graph | Repeat | Maximum degree | Natural number | Upper bound | Graphic methods
**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 Î”<2 and D<1, find the maximum number N(Î”,D) of vertices in a graph of maximum degree Î” 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:**
**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:**
**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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**Reviewed:**
**Date:** 2009
**Subject:** 0802 Computation Theory and Mathematics | 0103 Numerical and Computational Mathematics | 0102 Applied Mathematics | Degree/diameter problem | Bipartite Moore graphs | Compounding of graphs
**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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**Reviewed:**
**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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**Reviewed:**
**Date:** 2009
**Subject:** Bipartite Moore bound | Bipartite Moore graphs | Defect | Degree diameter problem for bipartite graphs
**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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**Reviewed:**
**Date:** 2009
**Subject:** 0101 Pure Mathematics | 0802 Computation Theory and Mathematics | Moore graphs | Degree/diameter problem | Diameter 2 and defect
**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:**
**Date:** 2008
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/54112
**Reviewed:**
**Date:** 2008
**Subject:** 0101 Pure Mathematics | Almost Moore digraph | Integer programming | Number theory | Numerical methods | Problem solving | Selfrepeats | Vertex orders | Graph theory
**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:**
**Date:** 2008
**Subject:** 0101 Pure Mathematics | Moore bound | Undirected graphs | Numerical methods | Problem solving | Degree diameter problems | Graph theory
**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:**
**Date:** 2008
**Subject:** 0101 Pure Mathematics | Digraphs | Genetic algorithms | Moore bound | Out-degree | Simulated annealing | Optimal systems | Diameter problem | Graph theory
**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:**
**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:**
**Date:** 2008
**Subject:** 0101 Pure Mathematics | 0802 Computation Theory and Mathematics | 0103 Numerical and Computational Mathematics
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/67727
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