Cordial Labelings Of Some Wheel Related Graphs

Abstract

Let $G$ be a graph with vertex set $V$ and edge set $E$. A vertex labelling $f:V\to \{0,1\}$ induces an edge labelling $\overline{f}:E\to \{0,1\}$ defined by $\overline{f}(uv)=|f(u)–f(v)|$. Let $v_f(0),v_f(1)$ denote the number of vertices $v$ with $f(v)=0$ and $f(v)=1$ respectively. Let $e_f(0),e_f(1)$ be similarly defined. A graph is said to be cordial if there exists a vertex labeling $f$ such that $|v_f(0)–v_f(1)|\le 1$ and $|e_f(0)–e_f(1)|\le 1$. In this paper, we show that for every positive integer $t$ and $n$ the following families are cordial: (1) Helms $H_n$. (2) Flower graphs $F{L}_n$. (3) Gear graphs $G_n$. (4) Sunflower graphs $SF{L}_n$. (5) Closed helms $C{H}_n$. (6) Generalised closed helms $CH(t,n)$. (7) Generalised webs $W(t,n)$.