A Different Approach for Multi level Distance Labellings of Path Structure Networks

Authors

  • Laxman Saha

Abstract

For a positive integer
k
, a radio
k -labelling of a simple connected graph
G V E ? ( , )
is a mapping
f from the vertex set
V G( )
to a set of non-negative integers such that
| ( ) ( ) | 1 ( , ) f u f v k d u v ? ? ? ?
for each
pair of distinct vertices
u
and
v
of
G
, where
d u v ( , )
is the distance between
u
and
v
in
G
. The span of a
radio
k -coloring
f
, denoted by
( ) f
span G
, is defined as
( )
max
v V G ?
f v( )
and the radio
k -chromatic number of
G
, denoted by
( ) k
rc G
, is
min
f
{ ( )} f
span G
where the minimum is taken over all radio
k -labellings of
G
. In
this article, we present results of radio
k -chromatic number of path
P
n
for
k k n n n ? ? ? ? { 1, 2, 3}
in
different approach but simple way.

Published

2020-03-25

Issue

Section

Articles