ON THE TOTAL VERTEX IRREGULARITY STRENGTHS OF QUADTREES AND BANANA TREES
Abstract: A vertex-irregular
total k-labelling λ : V (G)[ E(G) −! f1; 2; :::; kg of a graph G is a labelling
of vertices and edges of G in such a way that for any differentvertices x and
y, their weights wt(x) and wt(y) are distinct. The weight wt(x) of a vertex x
is the sum of the label of x and the labels of all edges incident with x.The
minimum k for which a graph G has a vertex-irregular total k-labelling is
calledthe total vertex irregularity strength of G, denoted by tvs(G). In this
paper, wedetermined the total vertex irregularity strengths of all quadtrees
and all banana trees.
Author: Nurdin
Journal Code: jpmatematikagg120011
