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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]]>Graph labeling techniques
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Wed 11 Apr 2018 16:19:10 AEST]]>Edge irregular reflexive labeling of prisms and wheels
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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]]>On edge irregular reflexive labellings for the generalized friendship graphs
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Tue 04 Feb 2020 10:56:06 AEDT]]>Vertex irregular reflexive labeling of prisms and wheels
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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]]>Constructions of H-antimagic graphs using smaller edge-antimagic graphs
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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]]>