5 research outputs found
Relating broadcast independence and independence
An independent broadcast on a connected graph is a function such that, for every vertex of , the value is at
most the eccentricity of in , and implies that for
every vertex of within distance at most from . The broadcast
independence number of is the largest weight
of an independent broadcast on . Clearly,
is at least the independence number for every
connected graph . Our main result implies . We
prove a tight inequality and characterize all extremal graphs
Broadcasts on Paths and Cycles
A broadcast on a graph is a function such that for every vertex , where denotes the diameter of and the eccentricity of in . The cost of such a broadcast is then the value .Various types of broadcast functions on graphs have been considered in the literature, in relation with domination, irredundence, independenceor packing, leading to the introduction of several broadcast numbers on graphs.In this paper, we determine these broadcast numbers for all paths and cycles, thus answering a questionraised in [D.~Ahmadi, G.H.~Fricke, C.~Schroeder, S.T.~Hedetniemi and R.C.~Laskar, Broadcast irredundance in graphs. {\it Congr. Numer.} 224 (2015), 17--31]