11 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
Eccentric Coloring in graphs
he \emph{eccentricity} of a vertex is the maximum distance of to any other vertex of . A vertex is an \emph{eccentric vertex} of vertex if the distance from to is equal to . An \emph{eccentric coloring} of a graph is a function \emph{color}: such that\\
(i) for all , .\\
(ii) for all , .\\
The \emph{eccentric chromatic number} for a graph is the lowest number of colors for which it is possible to eccentrically color \ \ by colors: . In this paper, we have considered eccentric colorability of a graph in relation to other properties. Also, we have considered the eccentric colorability of lexicographic product of some special class of graphs