On some classes of cycles-related $\Gamma$-harmonious graphs

Abstract

A graph $G(V,E)$ is $\Gamma$-harmonious when there is an injection $f$ from $V$ to an Abelian group $\Gamma$ such that the induced edge labels defined as $w(xy)=f(x)+f(y)$ form a bijection from $E$ to $\Gamma$. We study $\Gamma$-harmonious labelings of several cycles-related classes of graphs, including Dutch windmills, generalized prisms, generalized closed and open webs, and superwheels.