On the Locating-Chromatic Numbers of Non-Homogeneous Caterpillars and Firecracker Graphs

Abstract

We determine the locating-chromatic numbers of non-homogeneous caterpillars and firecracker graphs.

BILANGAN KROMATIK LOKASI UNTUK GRAF KEMBANG API F n, 2 DAN Fn, 3 DENGAN n ≥ 2

“…Graf kembang api (firecracker graph) F n,k adalah graf yang diperoleh dari n buah graf bintang S k dengan cara menghubungkan sebuah daun dari setiap S k melalui sebuah lintasan. Pada tulisan ini akan dikaji kembali mengenai penentuan bilangan kromatik lokasi dari graf kembang api F n,k untuk k = 2 dan k = 3 dengan n ≥ 2, seperti yang telah diperoleh dalam [2].…”

On the Locating Chromatic Number of Barbell Shadow Path Graph

“…Moreover, Chartrand et al [7] provided a tree construction of n vertices, n ≥ 5, with locating chromatic number varying from 3 to n, except for (n − 1). Next, Asmiati et al [1] obtained the locating chromatic number of amalgamation of stars and non-homogeneous caterpillars and firecracker graphs [2]. In [5] Welyyanti et al determined the locating chromatic number of complete n-ary trees.…”

On the Locating Chromatic Number of Certain Barbell Graphs

“…In [10] all trees of order with locating chromatic number − 1 were characterized, for any integers and , where > + 3 and 2 ≤ < /2. Asmiati et al in [11] have succeeded in determining the locating chromatic number of homogeneous amalgamation of stars and their monotonicity properties and in [12] for firecracker graphs. Next, Wellyyanti et al [13] determined the locating chromatic number for completeary trees.…”