Geodesic
On Distance Irregular Labeling of Disconnected Graphs
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 4, p. 507

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

A distance irregular $ k $-labeling of a graph $ G $ is a function $ f:V(G)\rightarrow\{1,2,…,k\} $ such that the weights of all vertices are distinct. The weight of a vertex $ v $, denoted by $ wt(v) $, is the sum of labels of all vertices adjacent to $ v $ (distance $ 1 $ from $ v $), that is, $ wt(v)=\sum_{u\in N(v)}f(u) $. If the graph $ G $ admits a distance irregular labeling then $ G $ is called a distance irregular graph. The distance irregularity strength of $ G $ is the minimum $ k $ for which $ G $ has a distance irregular $ k $-labeling and is denoted by $ \dis(G) $. In this paper, we derive a new lower bound of distance irregularity strength for graphs with $ t $ pendant vertices. We also determine the distance irregularity strength of some families of disconnected graphs namely disjoint union of paths, suns, helms and friendships.
Classification : 05C78
Keywords: Distance irregular labeling, disconnected graphs, paths, suns, helms, friendships 
Faisal Susanto; Kristiana Wijaya; Prasanti Mia Purnama; Slamin . On Distance Irregular Labeling of Disconnected Graphs. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 4, p. 507 . http://geodesic.mathdoc.fr/item/KJM_2022_46_4_a0/
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     title = {On {Distance} {Irregular} {Labeling} of {Disconnected} {Graphs}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {507 },
     year = {2022},
     volume = {46},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2022_46_4_a0/}
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