Mean Labelling on Some Graph

Abstract

This paper aims to prove that some certain graphs, such as triangular book graphs, ladder graphs, snail graphs, and Cartesian product graphs between cycles and paths, belong to the category of mean graphs. We chose these graph classes because it is still an open problem. To prove the above, we use two main approaches, such as the axiomatic descriptive method and the pattern detection method. The axiomatic descriptive method is used to describe the basic properties of graphs and organise them into formal arguments, while the pattern detection method is used to observe and generalise the structural properties of graphs in a more exploratory manner. Based in the results of the analysis and proof, we conclude that the four classes of graphs studied, to be triangular book graphs, ladder graphs, snail graphs, and Cartesian product graphs of cycles and paths, are proven to satisfy the characteristics of mean graphs.