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Critical injective chromatic graphs

The concept of critical injective chromatic graph is introduced. Some properties of critical injective chromatic graph are studied based on number of vertices and degree of graphs. The condition for cycles to be critical injective chromatic is obtained. The existence of a critical injective chromatic graph is established. An algorithm for injective colouring of vertices of a given connected graph is proposed. An application of injective chromatic number and injective chromatic sum in the diagnosis of diseases based on symptoms is suggested.