https://ogma.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:31448 Wed 11 Apr 2018 16:43:14 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:33940 Wed 04 Sep 2019 10:04:28 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:50434 Tue 25 Jul 2023 19:08:37 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:31515 v of a connected graph G (V, E) and a subset S of V, the distance between v and S is defined by d(v,S)=min{d(v,x):x∈S}. For an ordered k.-partition Π={S₁,S₂,…,S_k} of V, the representation of v with respect to Π is the k-vector r(v∣Π)=(d(v,S₁),d(v,S₂),…,d(v,S_k)). The k-partition Π is a resolving partition if the k-vectors r(v∣Π), v∈V are distinct. The minimum k for which there is a resolving k-partition of V is the partition dimension of G. In this paper, we obtain the partition dimension of circulant graphs [formula cannot be replicated]]]> Sat 24 Mar 2018 08:43:35 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:17583 Sat 24 Mar 2018 08:03:58 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:21856 1,...,w_k) be an ordered subset of V. The k-vector r(v|W)=(d(v,w₁),...,d(v,w_k)) is called the metric representation of v with respect to W. The set W is a resolving set of G if r(u|W) = r(v|W) implies u = v. The minimum cardinality of a resolving set in G is the metric dimension of G. In this paper we extend the notion of metric dimension to hypergraphs. We also introduce the dual concept, that is, edge dimension for hypergraphs, and initiate a study on this parameter.]]> Sat 24 Mar 2018 07:59:12 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:20385 Sat 24 Mar 2018 07:58:08 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:19436 Sat 24 Mar 2018 07:51:58 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:28278 metric basis. Metric dimension is the cardinality of a metric basis. A pair of vertices u, v is said to be strongly resolved by a vertex s, if there exists at least one shortest path from s to u passing through v, or a shortest path from s to v passing through u. A set W ⊆ V, is said to be a strong resolving set if for all pairs u, v ∉ W, there exists some element s ∈ W such that s strongly resolves the pair u, v. A strong resolving set of minimum cardinality is called a strong metric basis. The cardinality of a strong metric basis for G is called the strong metric dimension of G. The strong metric dimension (metric dimension) problem is to find a strong metric basis (metric basis) in the graph. In this paper, we solve the strong metric dimension and the metric dimension problems for the graph of tetrahedral diamond lattice.]]> Sat 24 Mar 2018 07:41:22 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:23752 f(G)=min{|g|:g is a minimal resolving function of G}, where |g|=∑v∈Vg(v). In this paper we study this parameter.]]> Sat 24 Mar 2018 07:11:10 AEDT ]]>