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  • Agustin, Ika Hesti  (2)
  • 1
    Online Resource
    Online Resource
    The reflexive vertex strength on cycle and generalized friendship graph
    World Scientific Pub Co Pte Ltd ; 2023
    In:  Asian-European Journal of Mathematics Vol. 16, No. 08 ( 2023-08)
    Details
    In: Asian-European Journal of Mathematics, World Scientific Pub Co Pte Ltd, Vol. 16, No. 08 ( 2023-08)
    Abstract: Let [Formula: see text] be a simple, un-directed and connected graph. The graph [Formula: see text] has a pair of sets [Formula: see text], where [Formula: see text] is nonempty vertex set and [Formula: see text] is an unordered pair of sets with two distinct vertices [Formula: see text] in [Formula: see text]. A total [Formula: see text] -labeling is defined as a function [Formula: see text] from the edge set to a set [Formula: see text] and a function [Formula: see text] from the vertex set to a set [Formula: see text] , where [Formula: see text]. The total [Formula: see text] -labeling is a vertex irregular reflexive[Formula: see text]-labeling of the graph [Formula: see text] , if for every two different vertices [Formula: see text] and [Formula: see text] of [Formula: see text], [Formula: see text] , where [Formula: see text]. The reflexive vertex strength of the graph [Formula: see text] , denoted by [Formula: see text] is the minimum [Formula: see text] for graph [Formula: see text] which has a vertex irregular reflexive [Formula: see text] -labeling. In this paper, we determined the exact value of the reflexive vertex strength of cycle and generalized friendship graph.
    Type of Medium: Online Resource
    ISSN: 1793-5571 , 1793-7183
    URL: Article
    DOI: 10.1142/S1793557123501371
    Language: English
    Publisher: World Scientific Pub Co Pte Ltd
    Publication Date: 2023
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  • 2
    Online Resource
    Online Resource
    The Distance Irregular Reflexive k-Labeling of Graphs
    Maulana Malik Ibrahim State Islamic University ; 2023
    In:  CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol. 7, No. 4 ( 2023-05-24), p. 622-630
    Details
    In: CAUCHY: Jurnal Matematika Murni dan Aplikasi, Maulana Malik Ibrahim State Islamic University, Vol. 7, No. 4 ( 2023-05-24), p. 622-630
    Abstract: A total k-labeling is a function fe from the edge set to the set {1, 2, . . . , ke} and a function fv from the vertex set to the set {0, 2, 4, . . . , 2kv}, where k = max{ke, 2kv}. A distance irregular reflexive k-labeling of the graph G is the total k-labeling, if for every two different vertices u and u 0 of G, w(u) 6= w(u 0 ), where w(u) = Σui∈N(u)fv(ui) + Σuv∈E(G)fe(uv). The minimum k for graph G which has a distance irregular reflexive k-labelling is called distance reflexive strength of the graph G, denoted by Dref (G). In this paper, we determine the exact value of distance reflexive strength of some connected graphs, namely path, star, and friendship graph.
    Type of Medium: Online Resource
    ISSN: 2477-3344 , 2086-0382
    URL: Article
    DOI: 10.18860/ca.v7i4.19747
    Language: Unknown
    Publisher: Maulana Malik Ibrahim State Islamic University
    Publication Date: 2023
    detail.hit.zdb_id: 2856372-4
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