On the total restrained double Italian domination
Publish place: The Journal of Algebra and Related Topics، Vol: 12، Issue: 1
Publish Year: 1403
نوع سند: مقاله ژورنالی
زبان: English
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JR_JART-12-1_009
تاریخ نمایه سازی: 31 تیر 1403
Abstract:
A double Italian dominating (DID) function of a graph G=(V,E) is a function f: V(G)\to\{۰,۱,۲,۳\} havingthe property that for every vertex v\in V, \sum_{u\in N_G[v]}f(u)\geq ۳, if f(v)\in \{۰,۱\}.A restrained double Italian dominating (RDID) function is a DID function f such that the subgraph induced by the verticeswith label ۰ has no isolated vertex.A total restrained double Italian dominating (TRDID) function is an RDID function f such that the set \{v\in V: f(v)> ۰\} induces a subgraph with no isolated vertex.\\We initiate the study of TRDID function of any graph G. The TRDID and RDID functions of the middle of any graph G are investigated,and then, the sharp bounds for these parameters are established.Finally, for a graph H, we provide the minimum value of TRDID and RDID functions for corona graphs,H \circ K_۱, H \circ K_۲ and middle of them.
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Authors
D. A. Mojdeh
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
M. Abdallah
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran