Finding the Number of Weak Homomorphisms of Paths

Abstract

Let $G$ and $H$ be graphs. A mapping $f$ from $V\left(G\right)$ to $V\left(H\right)$ is called a weak homomorphism from $G$ to $H$ if $f\left(x\right)=f\left(y\right)$ or $\left\{f\left(x\right),f\left(y\right)\right\}\in E\left(H\right)$ whenever $\left\{x,y\right\}\in E\left(G\right)$ . In this paper, we provide an algorithm to determine the number of weak homomorphisms of paths.