ON THE TOTAL IRREGULARITY STRENGTH OF AMALGAMATION OF STARS, BANANA TREES, AND FRIENDSHIP GRAPHS

• Main Author: IMELDA TILUKAY (NIM: 20110023), MEILIN
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/16416
• Institution: Institut Teknologi Bandung

The totally irregular total labeling was introduced by Marzuki, Salman, and Miller in (17). It is motivated by vertex irregular total labeling and edge irregular total <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> labeling introduced by Baca, Jendrol, Miller, and Ryan in (4). Let G = (V,E) be a graph. A function f : V U S <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> f : V U E -> (1,2, ...,k) of a graph G is a totally irregular total k-labeling if for any two different vertices x and y of G, their weights w(x) and w(y) are distinct and for any two different edges xy and uv of G, their weights w(xy) and w(uv) are distinct, where the weight w(x) of a vertex x is the sum of the label of x and the labels of all edges incident with x, and the weight w(xy) of an edge xy is the sum of the label of edge xy and the labels of vertices x and y. The minimum k for which a graph G has a totally irregular total k-labeling is called the total irregularity strength of G, denoted by ts(G). In this paper, we determine <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> the total irregularity strength for amalgamation of stars, banana trees, and friendship graphs.