Local Inclusive Distance Vertex Irregular Graphs

Kiki Ariyanti Sugeng, Denny Riama Silaban, Martin Bača and Andrea Semaničová-Feňovčíková
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Kiki Ariyanti Sugeng: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Kampus UI Depok, Depok 16424, Indonesia
Denny Riama Silaban: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Kampus UI Depok, Depok 16424, Indonesia
Martin Bača: Department of Applied Mathematics and Informatics, Technical University, 042 00 Košice, Slovakia
Andrea Semaničová-Feňovčíková: Department of Applied Mathematics and Informatics, Technical University, 042 00 Košice, Slovakia

Mathematics, 2021, vol. 9, issue 14, 1-12

Abstract: Let G = ( V , E ) be a simple graph. A vertex labeling f : V ( G ) ? { 1 , 2 , ? , k } is defined to be a local inclusive (respectively, non-inclusive) d -distance vertex irregular labeling of a graph G if for any two adjacent vertices x , y ? V ( G ) their weights are distinct, where the weight of a vertex x ? V ( G ) is the sum of all labels of vertices whose distance from x is at most d (respectively, at most d but at least 1). The minimum k for which there exists a local inclusive (respectively, non-inclusive) d -distance vertex irregular labeling of G is called the local inclusive (respectively, non-inclusive) d -distance vertex irregularity strength of G . In this paper, we present several basic results on the local inclusive d -distance vertex irregularity strength for d = 1 and determine the precise values of the corresponding graph invariant for certain families of graphs.

Keywords: (inclusive) distance vertex irregular labeling; local (inclusive) distance vertex irregular labeling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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