RT journal article
T1 Further results on packing related parameters in graphs
A1 Mojdeh, Doost Ali
A1 Samadi, Babak
A1 González Yero, Ismael
A2 Matemáticas
K1 packing number
K1 open packing number
K1 independence number
K1 Nordhaus-Gaddum inequality
K1 total domination number
AB Given a graph G = (V, E), a set B subset of V (G) is a packing in G if the closed neighborhoods of every pair of distinct vertices in B are pairwise disjoint. The packing number rho(G) of G is the maximum cardinality of a packing in G. Similarly, open packing sets and open packing number are defined for a graph G by using open neighborhoods instead of closed ones. We give several results concerning the (open) packing number of graphs in this paper. For instance, several bounds on these packing parameters along with some Nordhaus-Gaddum inequalities are given. We characterize all graphs with equal packing and independence numbers and give the characterization of all graphs for which the packing number is equal to the independence number minus one. In addition, due to the close connection between the open packing and total domination numbers, we prove a new upper bound on the total domination number gamma(t)(T) for a tree T of order n >= 2 improving the upper bound gamma(t)(T) <= (n + s)/2 given by Chellali and Haynes in 2004, in which s is the number of support vertices of T.
PB UNIV ZIELONA GORA
SN 1234-3099
YR 2022
FD 2022-05
LK http://hdl.handle.net/10498/26650
UL http://hdl.handle.net/10498/26650
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 13-nov-2026