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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Radio Antipodal Number of Certain Graphs
verfasst von : Albert William, Charles Robert Kenneth
Erschienen in: Informatics Engineering and Information Science
Verlag: Springer Berlin Heidelberg
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Let
G
= (
V
,
E
) be a graph with vertex set
V
and edge set
E
. Let
diam
(
G
) denote the diameter of
G
and
d
(
u
,
v
) denote the distance between the vertices
u
and
v
in
G
. An antipodal labeling of
G
with diameter
d
is a function
f
that assigns to each vertex
u
, a positive integer
f
(
u
), such that
d
(
u
,
v
) + |
f
(
u
) –
f
(
v
)| ≥
d
, for all
u
,
v
∈
V
. The span of an antipodal labeling
f
is
max
{|
f
(
u
) –
f
(
v
)|:
u
,
v
∈
V
(
G
)}. The antipodal number for
G
, denoted by
an
(
G
), is the minimum span of all antipodal labelings of
G
. Determining the antipodal number of a graph
G
is an NP-complete problem. In this paper we determine the antipodal number of certain graphs.