https://nova.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 Note on edge irregular reflexive labelings of graphs https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:44976 G, an edge labeling fe : E(G) → {1, 2, . . . , ke} and a vertex labeling fv : V(G) → {0, 2, 4, . . . , 2kv} are called total k-labeling, where k = max{ke, 2kv}. 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) = fv(x) + fe(xy) + fv(y) ̸= wt(x′ y′) = fv(x′) + fe(x′ y′) + fv(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 ]]> H-supermagic labelings for firecrackers, banana trees and flowers https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:30480 G = (V,E) admits an H-covering if every edge in E is contained in a subgraph H’= (V’, E’) of G which is isomorphic to H. In this case we say that G is H-supermagic if there is a bijection f : VE → {1,...,|V| + |E|} such that f(V) = {1,...,|V|} and ∑vϵV(H')f(v)+∑vϵV(H')f(e) is constant over all subgraphs H' of G which are isomorphic to H. Extending results from [M. Roswitha and E.T. Baskoro, Amer. Inst. Physics Conf. Proc. 1450 (2012), 135-138], we show that the firecracker Fk,n is F2,n-supermagic, the banana tree Bk,n is Bk-1,n-supermagic and the flower Fn is C3-supermagic.]]> Wed 11 Apr 2018 14:06:23 AEST ]]> Magic and Antimagic Graphs. Attributes, Observations and Challenges in Graph Labelings https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:45866 Mon 07 Nov 2022 15:55:14 AEDT ]]>