CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Vol 3, No 2 (2022): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS

Pewarnaan Sisi Ketakteraturan Lokal Refleksif pada Keluarga Graf Planar

Nuwaila Izzatul Muttaqi (Jember University)
Dafik Dafik (Unknown)
Robiatul Adawiyah (Unknown)



Article Info

Publish Date
01 Dec 2022

Abstract

All graph in this paper is simple and connected graph where $V(G)$ is vertex set and $E(G)$ is edge set. Let function $f : V(G)\longrightarrow \{0, 2,..., 2k_v\}$ as vertex labeling and a function $f: E(G)\longrightarrow \{1, 2,..., k_e\}$ as edge labeling where $k=max\{2k_v,k_e\}$ for $k_v,k_e$ are natural number. The weight of edge $ u,v\in E(G) $ under $f$ is $w(u)=f(u)+ \Sigma_{uv \in V(G)} f(uv)$. In other words, the function $f$ is called local edge irregular reflexive labeling if every two adjacent edges has distinct weight and weight of a edge is defined as the sum of the labels of edge and the labels of all vertex incident this edge When we assign each edge of $G$ with a color of the edge weight $w(uv)$, thus we say the graph $G$ admits a local edge irregular reflexive coloring. The minimum number of colors produced from local edge irregular reflexive coloring of graph $G$ is reflexive local irregular chromatic number denoted by $\chi_{lrecs}(G).$ Furthermore, the minimum $k$ required such that $\chi_{lrecs}(G)=\chi(G)$ is called a local reflexive edge color strength, denoted by \emph{lrecs}$(G)$. In this paper, we learn about the local edge irregular reflexive coloring and obtain \emph{lrecs}$(G)$ of planar related graphs.

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Journal Info

Abbrev

cgant

Publisher

Subject

Computer Science & IT Other

Description

Subjects suitable for publication include, the following fields of: Degree Diameter Problem in Graph Theory Large Graphs in Computer Science Mathematical Computation of Graph Theory Graph Coloring in Atomic and Molecular Graph Labeling in Coding Theory and Cryptography Dimensions of graphs on ...