ON ITALIAN DOMINATION NUMBER OF UNARY OPERATIONS OF SPECIAL GRAPHS

ON ITALIAN DOMINATION NUMBER OF UNARY OPERATIONS OF SPECIAL GRAPHS

A. Prakash, P. Ragukumar

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Abstract

For a graph G = (V,E), an Italian dominating function (IDF) f : V ā†’ {0, 1, 2} has the property that for every vertex v āˆˆ V with f(v) = 0, either v is adjacent to a vertex assigned 2 under f, or v is adjacent to at least two vertices assigned 1 under f. The weight of an Italian dominating function is the P vāˆˆV f(v), and the minimum weight of a Italian dominating function f is the Italian domination number. This study illustrates the Italian domination number of graphs that are generated when various unary operations are applied to standard graph classes.

Keywords

Domination, Roman domination, Italian dominating function, Italian domination number.