Discrete Labeling of Graphs

Objectives: To introduce a new type of labeling called Discrete Labeling. This labeling aims at providing the maximum output whenever the inputs are distinct with rational distribution of neighbours thereby exhibiting the stronger form of Cordial labeling. This work serves as an aid in decision-making. Methods: The discrete labels 0 and 1 are cordially assigned to the vertices such that the edges receive labels depending on the incident vertex labels using EX-OR operation with the condition that for every vertex the cardinality of neighbours labeled 0 and 1 differs by at most 1. Findings: This study proposes the discrete labeling of some standard and special graphs. Also it provides the cases for which certain path, star and cycle related graphs admit discrete labeling. Novelty: This labeling uses EX-OR operation which reduces the complexity of having two swords in one sheath. Apart from keeping the distinct vertex labels and edge labels difference minimal, the cardinality of the neighbouring labels of every vertex is also taken into account. Keywords: Graph Parameters, Discrete, Trees, Cycle, Complete Graphs