TY  - JOUR
ID  - Susanto2022
LB  - Susanto2022
AU  - Susanto, Faisal
AU  - Wijaya, Kristiana
AU  - Slamin
AU  - Semaničová-Feňovčíková, Andrea
TI  - Distance irregularity strength of graphs with pendant vertices
ST  - Distance irregularity strength of graphs with pendant vertices
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2022
VL  - 42
IS  - 3
SP  - 439
EP  - 458
DO  - https://doi.org/10.7494/OpMath.2022.42.3.439
UR  - https://doi.org/10.7494/OpMath.2022.42.3.439
AB  - A vertex \(k\)-labeling \(\phi:V(G)\rightarrow\{1,2,\dots,k\}\) on a simple graph \(G\) is said to be a distance irregular vertex \(k\)-labeling of \(G\) if the weights of all vertices of \(G\) are pairwise distinct, where the weight of a vertex is the sum of labels of all vertices adjacent to that vertex in \(G\). The least integer \(k\) for which \(G\) has a distance irregular vertex \(k\)-labeling is called the distance irregularity strength of \(G\) and denoted by \(\mathrm{dis}(G)\). In this paper, we introduce a new lower bound of distance irregularity strength of graphs and provide its sharpness for some graphs with pendant vertices. Moreover, some properties on distance irregularity strength for trees are also discussed in this paper.
KW  - vertex \(k\)-labeling
KW  - distance irregular vertex \(k\)-labeling
KW  - distance irregularity strength
KW  - pendant vertices
SN  - 1232-9274
ER  -