https://nova.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:11375 Sat 24 Mar 2018 08:11:55 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:29034 G = (V, E) be a graph. A function f : V∪E → {1, 2, ..., k} of a graph G is a totally irregular total k-labeling if for any two different vertices x and y of G, their weights wt(x) and wt(y) are distinct and for any two different edges x₁x₂ and y₁y₂ of G, their weights wt(x₁x₂) and wt(y₁y₂) are distinct, where the weight wt(x) of a vertex x is the sum of the label of x and the labels of all edges incident with x, and the weight wt(x₁x₂) of an edge x₁x₂ is the sum of the label of edge x₁x₂ and the labels of vertices x₁ and x₂. The minimum k for which a graph G has a totally irregular total k-labeling is called the total irregularity strength of G, denoted by ts(G). In this paper, we provide an upper bound and a lower bound of the total irregularity strength of a graph. Besides that, we determine the total irregularity strength of cycles and paths.]]> Sat 24 Mar 2018 07:37:15 AEDT ]]>