The L(3; 2; 1) Labeling of Some Expanded Graphs

• Main Author: Nur Alifah, Amalia
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/42230
• Institution: Institut Teknologi Bandung

Let G = (V;E) be a nontrivial and connected graph. The L(3; 2; 1) labeling of graph G is a function f : V ! N [ f0g such that jf(u) ???? f(v)j 3 for every u; v 2 V with d(u; v) = 1, jf(u) ???? f(v)j 2 for every u; v 2 V with d(u; v) = 2, and jf(u) ???? f(v)j 1 for every u; v 2 V with d(u; v) = 3. For natural number k, a k ???? L(3; 2; 1) labeling is an L(3; 2; 1) labeling such that no label is greater than k. The L(3; 2; 1) number of G, denoted by 3;2;1(G) is the smallest number k such that G has a k ???? L(3; 2; 1) labeling. In this thesis, we give the 3;2;1 number of a book graph Bn, an expanded graph by book graph Bm and path graph Pn, and an expanded graph by cycle graph Cm and path graph Pn.