Central graphs and Italian domination parameters

• Published in: Journal of Kufa for Mathematics and Computer 2024-03, Vol.11 (1), p.15-24
• Main Authors: Abdulhasan, Alaa, Mojdeh, Doost Ali
• Format: Article
• Language: English
• ISSN: 2076-1171; 2518-0010
• DOI: 10.31642/JoKMC/2018/110104

Abstract     Let  be a graph with and A function is said to be an Italian dominating function on a graph  if every vertex  with is adjacent to at least one vertex  with or is adjacent to at least two vertices  with . The value denotes the weight of an Italian dominating function.  The minimum weight taken over all Italian dominating functions of  is called Italian domination number and denoted by        Two parameters related to Italian dominating function are restrained Italian and total restrained dominating functions  , for which the set of vertices  with , and simultaneously the set of vertices  with and the set of vertices  with induce subgraphs with no isolated vertex respectively. The central graph of a graph  is the graph obtained by subdividing each edge of  exactly once and joining all the non-adjacent vertices of      In this work, we initiate the study of restrained (total restrained) Italian domination number of the central of any graph  For a family of standard graphs  we obtain the precise value of restrained (total restrained) Italian domination number for indeed for any graph G, the sharp bounds are provided for and for  corona of ,  we establish the precise value of these parameters for