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 
@article{KJM_2022_46_4_a0,
     author = {Faisal Susanto and Kristiana Wijaya and Prasanti Mia Purnama and Slamin },
     title = {On {Distance} {Irregular} {Labeling} of {Disconnected} {Graphs}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {507 },
     publisher = {mathdoc},
     volume = {46},
     number = {4},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2022_46_4_a0/}
}
TY  - JOUR
AU  - Faisal Susanto
AU  - Kristiana Wijaya
AU  - Prasanti Mia Purnama
AU  - Slamin 
TI  - On Distance Irregular Labeling of Disconnected Graphs
JO  - Kragujevac Journal of Mathematics
PY  - 2022
SP  - 507 
VL  - 46
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KJM_2022_46_4_a0/
LA  - en
ID  - KJM_2022_46_4_a0
ER  - 
%0 Journal Article
%A Faisal Susanto
%A Kristiana Wijaya
%A Prasanti Mia Purnama
%A Slamin 
%T On Distance Irregular Labeling of Disconnected Graphs
%J Kragujevac Journal of Mathematics
%D 2022
%P 507 
%V 46
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KJM_2022_46_4_a0/
%G en
%F KJM_2022_46_4_a0
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/