Vertex-Irregular Labeling and Vertex-Irregular Total Labeling on Caterpillar Graph
Nurdin Nurdin, Muh. Zakir, Firman Firman · Hasanuddin University Repository · 2013
For a simple graph $G$ with the vertex set $V$ and the edge set $E$, a labeling $\\lambda : V(G) \\cup E(G) \\longrightarrow \\{1, 2, \\cdots, k\\}$ is called a vertex irregular total $k$-labeling of $G$ if for any two different vertices $x$ and $y$ in $V$ we have $wt(x) \ eq wt(y)$ where $wt(x)=\\lambda (x) + \\sum_{z \\in V}\\lambda(xz)$. The total vertex irregularity strength of $G$, denoted by $tvs(G)$, is the smallest positive integer $k$ for which $G$ has a vertex irregular total $k-$labeling. In this paper, we determined the total vertex irregularity strength of a caterpillar graph.