Open AccessBILANGAN KROMATIK LOKASI UNTUK GRAF AMALGAMASI BINTANG
Author(s) -
Syamsi Fadhilah
Publication year - 2013
Publication title -
jurnal matematika unand/jurnal matematika unand
Language(s) - English
Resource type - Journals
eISSN - 2721-9410
pISSN - 2303-291X
DOI - 10.25077/jmu.2.1.6-13.2013
Subject(s) - combinatorics , vertex (graph theory) , graph , star (game theory) , physics , mathematics , edge coloring , astrophysics , graph power , line graph
Let G = (V; E) be a connected graph and c a coloring of G. For i = 1; 2; :::; k,we dene the color classes Cias the set of vertices receiving color i. The color code c(v)of a vertex v 2 V (G) is the k-vector (d(v; C1); d(v; C2); :::; d(v; Ck)), where d(v; C) isthe distance between v and C. If all vertices of G have distinct color codes, then c iscalled a locating-coloring of G. The locating-coloring number of graph G, denoted byLi(G), is the smallest positive integer k such that G has a locating coloring with k color.Let K1;nibe star, where niis the number of leaves of each star K. We dene thevertex amalgamation of star, denoted by Sk;(n1;:::;nk)1;n, as a graph obtained from starsKby identifying one arbitrary leaf from each star. We dene the edge amalgamationof star, denoted by S1;nik;(n, as a graph obtained by uniting an edge of each star.If ni1;:::;nk)= m for each i, then we denoted the vertex amalgamation of star as Sandthe edge amalgamation of star as Sk;m. In this paper we discuss the locating coloring ofSk;(n1;:::;nk)and Sk;(n1;:::;nk).