https://ogma.newcastle.edu.au/vital/access/ /manager/Index en-au 5 https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:51826 Wed 20 Sep 2023 10:07:32 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:7777 Wed 11 Apr 2018 17:19:24 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:9139 Wed 11 Apr 2018 17:07:23 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:19143 Wed 11 Apr 2018 15:42:23 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:15027 Wed 11 Apr 2018 11:54:21 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:4997 Wed 11 Apr 2018 10:44:45 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:30797 Wed 11 Apr 2018 10:36:06 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:33000 k(G), is defined as the cardinality of a minimum k-restricted edge cut. A connected graph G is said to be λ_k-connected if G has a k-restricted edge cut. Let ξ_k(G) = min{|[X, ̅X ]| : |X| = k, G[X] is connected}, where ̅X = V (G)X. A graph G is said to be maximally k-restricted edge connected if λ_k(G) = ξ_k(G). In this paper we show that if G is a λ₄-connected graph with λ₄(G) ≤ ξ₄(G) and the girth satisfies g(G) ≥ 8, and there do not exist six vertices u₁, u₂, u₃, v₁, v₂ and v₃ in G such that the distance d(u_i, v_j) ≥ 3, (1 ≤ i, j ≤ 3), then G is maximally 4-restricted edge connected.]]> Tue 03 Sep 2019 18:17:58 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:28963 Thu 26 Jul 2018 16:56:33 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:9422 2.]]> Sat 24 Mar 2018 08:39:18 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:8860 Sat 24 Mar 2018 08:39:02 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:8862 Sat 24 Mar 2018 08:39:02 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:8859 Sat 24 Mar 2018 08:39:01 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:8136 Sat 24 Mar 2018 08:36:10 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:1158 Sat 24 Mar 2018 08:28:43 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:21870 Sat 24 Mar 2018 07:52:57 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:5965 2.]]> Sat 24 Mar 2018 07:47:27 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:5973 Sat 24 Mar 2018 07:47:24 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:5916 Sat 24 Mar 2018 07:46:46 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:6126 Sat 24 Mar 2018 07:44:30 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:68 Sat 24 Mar 2018 07:42:02 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:27706 spectrum. The energy of a graph is the sum of the absolute values of its eigenvalues. In this paper, we devise an algorithm which generates the adjacency matrix of WK - recursive structures WK(3,L) and WK(4,L) and use it in the effective computation of spectrum and energy.]]> Sat 24 Mar 2018 07:40:10 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:24680 0, making it significantly harder than Dominating Set, while it remains hard even on severely restricted special cases, such as cubic graphs (APX-hard), and planar subcubic graphs (NP-hard). We complement our negative results by showing that the problem admits an O(Δ) approximation on graphs of maximum degree Δ, as well as an EPTAS on planar graphs. Along the way, we also derive essentially tight n1−1d upper and lower bounds on the approximability of the related problem Maximum Minimal Hitting Set on d-uniform hypergraphs, generalising known results for Maximum Minimal Vertex Cover.]]> Sat 24 Mar 2018 07:10:51 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:44902 Mon 24 Oct 2022 16:10:33 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:32758 sum graph G is a graph with an injective mapping of the vertex set of G onto a set of positive integers S in such a way that two vertices of G are adjacent if and only if the sum of their labels is an element of S. In an exclusive sum graph the integers of S that are the sum of two other integers of S form a set of integers that label a collection of isolated vertices associated with the graph G. A graph bears a k-exclusive sum labelling (abbreviated k-ESL), if the set of isolated vertices is of cardinality k, an optimal exclusive sum labelling, if k is as small as possible, and Δ-optimal if k equals the maximum degree of the graph. In this paper, observing that the property of having a k-ESL is hereditary, we provide a characterisation of graphs that have a k-exclusive sum labelling, for any k ≥ 1, in terms of describing a universal graph for the property.]]> Mon 23 Jul 2018 11:04:20 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:51379 Mon 15 Jan 2024 15:15:51 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:30752 G and the graph G + K₁. Finally, we determine the distance irregularity strength of m-book graphs B_m.]]> Fri 06 Oct 2023 15:48:06 AEDT ]]>