Open AccessOn local irregularity vertex coloring of comb product on star graphs
Author(s) -
I. L. Mursyidah,
Dafik Dafik,
Robiatul Adawiyah,
Arika Indah Kristiana,
Ika Hesti Agustin
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1836/1/012023
Subject(s) - combinatorics , vertex (graph theory) , neighbourhood (mathematics) , mathematics , fractional coloring , bipartite graph , graph , complete bipartite graph , graph power , discrete mathematics , line graph , mathematical analysis
Let G = (V,E) be a graph with vertex set V and edge set E. The graph G is said to be a local irregular vertex coloring if there is a function f is a called a local irregularity vertex coloring if : (i) l : (V (G)) → {1, 2,…,k} as a vertex irregular k-labeling and w : V(G) → N, for every uv ∈ E(G),w(u) = w(v) where w(u) = Σ v ∈N ( u ) l(i) and (ii) opt (I) = min{rnax{li; livertex irregular labeling }}. The chromatic number of local irregularity vertex coloring of G denoted by Xl is (G), is the minimum cardinality of the largest label over all such local irregularity vertex coloring. In this paper, we study local irregular vertex coloring of G ⊳ ∘ S n when G is complete bipartite graph (K m , p ), ladder graph (L m ), fan graph (F m ), friendship graph (Fr m ), and cycle graph (C m ).