$L(3, 2, 1)$-LABELING OF SOME CYCLE RELATED GRAPHS

Abstract

Let $G=(V(G), E(G))$ be a connected graph. For $i,j,k\in \mathbb{N}$ with $i\geq j \geq k$, $L(i, j, k)$-labeling of graph $G$ is an integer labeling of the vertices of graph $G$ such that labels of adjacent vertices differ by at least $i$, labels of vertices at distance two differ by at least $j$ and labels of vertices at distance three differ by at least $k$. In this paper, we discuss $L(3, 2, 1)$-labeling for crown, arm crown, tadpole, and closed helm graphs.