@article{e5099517c54a4eb096df437455f60108,

title = "Strong block-block domination of a graph",

abstract = "Let B(G) denotes the set of all blocks of a graph G. Two blocks in G are adjacent if there is a common cutvertex incident on them. Two blocks b1, b2 ∈ B(G) are said to bb-dominate each other if there is a common vertex incident with b1 and b2. A set L ⊆ B(G) is said to be a bb-dominating set (BBD set) if every block in G is bb-dominated by some block in L. The bb-domination number γbb = γbb(G) is the cardinality of a minimum bb-dominating set of G. In this paper we define strong (weak) bb-dominating set and strong (weak) bb-full set and obtained relationship between them. We also obtain the relation with existing graph parameters.",

author = "Sayinath Udupa and Bhat, {R. S.} and N. Prathviraj",

note = "Funding Information: We thank the members of JG laboratory for comments on the manuscript. We are grateful to Dr A Benmerah (Institut Necker, Paris, France) for the EPS15 constructs and helpful discussion and to C Catherinet (INSA, Rennes, France) for technical support. This research was funded by: ANR JCJC, Fondation ARC, Fondation pour la Recherche Medicale, INCA_6508, Ligue nationale contre le cancer comite de Paris and a Marie Curie International Reintegration Grant within The Seventh Framework Program. SA, SSS and JD are supported by postdoctoral fellowships from Fondation ARC, Canceropole Ile-de-France and ANRS, respectively. JKH is supported by a doctoral fellowship from Universite Paris Descartes. Publisher Copyright: {\textcopyright} 2022 Forum-Editrice Universitaria Udinese SRL. All rights reserved.",

year = "2022",

language = "English",

volume = "47",

pages = "1029--1036",

journal = "Italian Journal of Pure and Applied Mathematics",

issn = "1126-8042",

publisher = "Forum Societa Editrice Universitaria Udinese srl",

}