Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 9 2 2024 06 01 Leech Graphs 205 215 14452 10.22049/cco.2022.27735.1339 EN Seena Varghese Department of Mathematics, Federal Institute of Science and Technology, Angamaly-683577, Ernakulam District, Kerala, India Aparna Lakshmanan Savithri Department of Mathematics, Cochin University of Science and Technology,Cochin-22, Kerala,India S. Arumugam National Centre for Advanced Research in Discrete Mathematics, Kalasalingam University Anand Nagar, Krishnankoil-626 126, Tamil Nadu, India Journal Article 2022 03 31 Let $t_p(G)$ denote the number of paths in a graph $G$ and let $f:E\rightarrow \mathbb{Z}^+$ be an edge labeling of $G$. The weight of a path $P$ is the sum of the labels assigned to the edges of $P$. If the set of weights of the paths in $G$ is $\{1,2,3,\dots,t_p(G)\}$, then $f$ is called a Leech labeling of $G$ and a graph which admits a Leech labeling is called a Leech graph. In this paper, we prove that the complete bipartite graphs $K_{2,n}$ and $K_{3,n}$ are not Leech graphs and determine the maximum possible value that can be given to an edge in the Leech labeling of a cycle. https://comb-opt.azaruniv.ac.ir/article_14452_ce94194bfd3899e3f4e232d5f7967cf6.pdf