https://nova.newcastle.edu.au/vital/access/ /manager/Index en-au 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:44976 G, an edge labeling f_e : E(G) → {1, 2, . . . , k_e} and a vertex labeling f_v : V(G) → {0, 2, 4, . . . , 2k_v} are called total k-labeling, where k = max{k_e, 2k_v}. The total k-labeling is called an edge irregular reflexive k-labeling of the graph G, if for every two different edges xy and x′ y′ of G, one has wt(xy) = f_v(x) + f_e(xy) + f_v(y) ̸= wt(x′ y′) = f_v(x′) + f_e(x′ y′) + f_v(y′). The minimum k for which the graph G has an edge irregular reflexive k-labeling is called the reflexive edge strength of G. In this paper we determine the exact value of the reflexive edge strength for cycles, Cartesian product of two cycles and for join graphs of the path and cycle with 2K₂.]]> Wed 26 Oct 2022 08:53:34 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:31249 Wed 11 Apr 2018 16:19:10 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:30428 G we define k-labeling ρ such that the edges of G are labeled with integers {1, 2, . . . , k_e} and the vertices of G are labeled with even integers {0, 2, . . . , 2k_v}, where k = max{k_e, 2k_v}. The labeling ρ is called an edge irregular k-labeling if distinct edges have distinct weights, where the edge weight is defined as the sum of the label of that edge and the labels of its ends. The smallest k for which such labeling exist is called the reflexive edge strength of G. In this paper we give exact values of reflexive edge strength for prisms, wheels, baskets and fans.]]> Wed 11 Apr 2018 13:07:11 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:31129 Tue 04 Feb 2020 10:56:06 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:43783 G we define k-labeling ρ such that the edges of G are labeled with integers {1,2,…,k_e} and the vertices of G are labeled with even integers {0,2,…,2k_v}, where k=max{k_e,2k_v}. The labeling ρ is called a vertex irregular reflexive k-labeling if distinct vertices have distinct weights, where the vertex weight is defined as the sum of the label of that vertex and the labels of all edges incident this vertex. The smallest k for which such labeling exists is called the reflexive vertex strength of G.]]> Thu 29 Sep 2022 13:48:03 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:34916 antimagic labeling of G admitting an H-covering is a bijective function f : V ∪ E → {1, 2, ..., ∣V∣ + ∣E∣} such that, for all subgraphs H' of G isomorphic to H, the H'-weights, et_f(H') = Σ_υ∈V(H')f(υ)+Σ_e∈E(H')F(e), constitute an arithmetic progression with the initial term a and the common difference d. Such a labeling is called super if f(V) = {1, 2, ..., ∣V∣}. In this paper, we study the existence of super (a, d)-H-antimagic labelings for graph operation G^H, where G is a (super) (b, d*)-edge-antimagic total graph and H is a connected graph of order at least 3.]]> Fri 06 Oct 2023 15:46:50 AEDT ]]>