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${session.getAttribute("locale")}5Note on edge irregular reflexive labelings of graphs
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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 2K_{2}.]]>Wed 26 Oct 2022 08:53:34 AEDT]]>H-supermagic labelings for firecrackers, banana trees and flowers
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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 : V ⋃ E → {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 F_{k,n} is F_{2,n}-supermagic, the banana tree B_{k,n} is B_{k-1,n}-supermagic and the flower F_{n} is C_{3}-supermagic.]]>Wed 11 Apr 2018 14:06:23 AEST]]>Magic and Antimagic Graphs. Attributes, Observations and Challenges in Graph Labelings
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