https://ogma.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:28348 Wed 11 Apr 2018 13:20:27 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:15630 Sat 24 Mar 2018 08:23:46 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11283 t and girth at least g ≥ t + 1. The set of all the graphs of order n, containing no cycles of length ≤ t, and of size ex(n; t), is denoted by EX(n; t) = EX(n; {C₃,C₄, . . . ,Cᵼ }), these graphs are called EX graphs. In 1975, Erdős proposed the problem of determining the extremal numbers ex(n; 4) of a graph of order n and girth at least 5. In this paper, we consider a generalized version of this problem, for t ≥ 5. In particular, we prove that ex(29; 6) = 45, also we improve some lower bounds and upper bounds of exᴜ(n; t), for some particular values of n and t.]]> Sat 24 Mar 2018 08:12:43 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:17756 ί, ί , i = 1, . . . , r of G is isomorphic to H and f(H_ί)=f(H)=Σ v∈V(H_ί) f(v)+Σ e∈V(H_ί) f(e)=m(f). In this paper we define a subgraph-vertex magic cover of a graph and give some construction of some families of graphs that admit this property. We show the construction of some C_n - vertex magic covered and clique magic covered graphs.]]> Sat 24 Mar 2018 07:57:21 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:17749 Sat 24 Mar 2018 07:57:20 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:28280 m,n is an example of join graphs and we give an antimagic labeling for K_m,n,n≥2m+1. In this paper we also provide constructions of antimagic labelings of some complete multipartite graphs.]]> Sat 24 Mar 2018 07:41:22 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:28611 Sat 24 Mar 2018 07:38:54 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:26777 Sat 24 Mar 2018 07:36:23 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:28309 1, diameter k > 1 and order N(d,k)=d+d²+...+d^k. So far, their existence has only been showed for k = 2. Their nonexistence has been proved for k = 3, 4 and for d = 2, 3 when k ≥ 3. In this paper, we prove that (4, k) and (5, k)-digraphs with self-repeats do not exist for infinitely many primes k.]]> Sat 24 Mar 2018 07:27:06 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:42816 Mon 05 Sep 2022 11:14:40 AEST ]]>