Jurnal Siger Matematika
Vol 2, No 2 (2021): Jurnal Siger Matematika

Bilangan Kromatik Lokasi Subdivisi Operasi Barbel Tertentu Graf Origami \mathbit{B}_{\mathbit{O}_\mathbf{3}}^\mathbit{s}, \mathbit{B}_{\mathbit{O}_\mathbf{4}}^\mathbit{s}, \mathbit{B}_{\mathbit{O}_\mathbf{5}}^\mathbit{s}, \mathbit{B}_{\mathbit{O}_\mathbf

Agus Iriawan (STMIK Pringsewu)
Asmiati Asmiati (Universitas Lampung)
La Zakaria (Universitas Lampung)
Kurnia Muludi (Universitas Lampung)
Bernadhita Herindri Samodra Utami (Unknown)



Article Info

Publish Date
30 Sep 2021

Abstract

Let G=(V,E) be a connected graph and c be a proper k-coloring of G with color 1,2,...,k. Let {C_1,C_2,...,C_k} be a partition of V(G) which is induced by coloring c. The color code c_Phi(v) of v is the ordered k-tuple (d(v,C_1),d(v,C_2),...,d(v,C_k)) where  d(v,C_i)= min{d(v,x)|x \in C_i}  for any i. If all distinct vertices of G have distinct color codes, then c is called  k-locating coloring of G. The locating-chromatic number, denoted by \chi_L(G), is the smallest k such that G has a locating k-coloring.  Subdivision certain barbell origami graphs, for s>=1, is a graph with  V\left(B_{O_n}^s\right)=\left\{u_i,u_{n+i},v_i,v_{n+i},w_i,w_{n+i}\middle|1\le i\le n\right\} U {x_i|1<=i<=s}  and E\left(B_{O_n}^s\right)={{u}_iw_i,u_iv_i,v_iw_i,u_iu_{i+1},w_iu_{i+1}|1\le i\le n} U {{u}_{n+i}w_{n+i},u_{n+i}v_{n+i},v_{n+i}w_{n+i},u_{n+i}u_{n+i+1},w_{n+i}u_{n+i+1}|1\le i\le n-1} U {u_nx_1,x_nu_{n+1}} U{x_ix_{i+1}|1\le i\le s-1}. In this paper, we will determined the locating-chromatic number of subdivision certain barbell origami graphs B_{O_3}^s,B_{O_4}^s , B_{O_5}^s and  B_{O_6}^s.

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Journal Info

Abbrev

JSM

Publisher

Subject

Mathematics

Description

Jurnal Siger Matematika is a broad scope journal that publishes original research articles as well as review articles on all aspects of both pure and applied mathematics. publised by Departement Mathematics, Faculty of Mathematics and Natural Sciences, University of Lampung. This journal covers all ...