Geodesic
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. 
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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     title = {On local irregularity of the vertex coloring of the corona product of a tree graph},
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     language = {en},
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[1] Fructh R., Harary F., “On the corona of two graphs”, Aequationes Math., 4 (1970), 322–325 | DOI

[2] Kristiana A. I., Dafik, Utoyo M. I., Slamin, Alfarisi R., Agustin I. H., Venkatachalam M., “Local irregularity vertex coloring of graphs”, Int. J. Civil Eng. Technol., 10:3 (2019), 1606–1616

[3] Kristiana A. I., Utoyo M. I., Dafik, Agustin I. H., Alfarisi R., Waluyo E., “On the chromatic number local irregularity of related wheel graph”, J. Phys.: Conf. Ser., 1211 (2019), 0120003, 1–10 | DOI

[4] Kristiana A. I., Alfarisi R., Dafik, Azahra N., “Local irregular vertex coloring of some families of graph”, J. Discrete Math. Sci. Cryptogr., 2020, 15–30 | DOI