On local irregularity of the vertex coloring of the corona product of a tree graph
Ural mathematical journal, Tome 8 (2022) no. 2, pp. 94-114
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Let $G=(V,E)$ be a graph with a vertex set $V$ and an edge set $E$. The graph $G$ is said to be with a local irregular vertex coloring if there is a function $f$ called a local irregularity vertex coloring with the properties: (i) $l:(V(G)) \to \{ 1,2,...,k \} $ as a vertex irregular $k$-labeling and $w:V(G)\to N,$ for every $uv \in E(G),$ ${w(u)\neq w(v)}$ where $w(u)=\sum_{v\in N(u)}l(i)$ and (ii) $\mathrm{opt}(l)=\min\{ \max \{ l_{i}: l_{i} \text{ is a vertex irregular labeling}\}\}$. The chromatic number of the local irregularity vertex coloring of $G$ denoted by $\chi_{lis}(G)$, is the minimum cardinality of the largest label over all such local irregularity vertex colorings. In this paper, we study a local irregular vertex coloring of $P_m\bigodot G$ when $G$ is a family of tree graphs, centipede $C_n$, double star graph $(S_{2,n})$, Weed graph $(S_{3,n})$, and $E$ graph $(E_{3,n})$.
Keywords:
local irregularity, corona product, tree graph family.
@article{UMJ_2022_8_2_a7,
author = {Arika Indah Kristiana and M. Hidayat and Robiatul Adawiyah and D. Dafik and Susi Setiawani and Ridho Alfarisi},
title = {On local irregularity of the vertex coloring of the corona product of a tree graph},
journal = {Ural mathematical journal},
pages = {94--114},
year = {2022},
volume = {8},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/UMJ_2022_8_2_a7/}
}
TY - JOUR AU - Arika Indah Kristiana AU - M. Hidayat AU - Robiatul Adawiyah AU - D. Dafik AU - Susi Setiawani AU - Ridho Alfarisi TI - On local irregularity of the vertex coloring of the corona product of a tree graph JO - Ural mathematical journal PY - 2022 SP - 94 EP - 114 VL - 8 IS - 2 UR - http://geodesic.mathdoc.fr/item/UMJ_2022_8_2_a7/ LA - en ID - UMJ_2022_8_2_a7 ER -
%0 Journal Article %A Arika Indah Kristiana %A M. Hidayat %A Robiatul Adawiyah %A D. Dafik %A Susi Setiawani %A Ridho Alfarisi %T On local irregularity of the vertex coloring of the corona product of a tree graph %J Ural mathematical journal %D 2022 %P 94-114 %V 8 %N 2 %U http://geodesic.mathdoc.fr/item/UMJ_2022_8_2_a7/ %G en %F UMJ_2022_8_2_a7
Arika Indah Kristiana; M. Hidayat; Robiatul Adawiyah; D. Dafik; Susi Setiawani; Ridho Alfarisi. On local irregularity of the vertex coloring of the corona product of a tree graph. Ural mathematical journal, Tome 8 (2022) no. 2, pp. 94-114. http://geodesic.mathdoc.fr/item/UMJ_2022_8_2_a7/
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