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Some Characterizations and NP-Complete Problems for Power Cordial Graphs
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A power cordial labeling of a graph
G
=
V
G
,
E
G
is a bijection
f
:
V
G
⟶
1,2
,
…
,
V
G
such that an edge
e
=
u
v
is assigned the label 1 if
f
u
=
f
v
n
or
f
v
=
f
u
n
, for some
n
∈
N
∪
0
and the label 0 otherwise, and satisfy the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. The graph that admits power cordial labeling is called a power cordial graph. In this paper, we derive some characterizations of power cordial graphs as well as explore NP-complete problems for power cordial labeling. This work also rules out any possibility of forbidden subgraph characterization for power cordial labeling.
Title: Some Characterizations and NP-Complete Problems for Power Cordial Graphs
Description:
A power cordial labeling of a graph
G
=
V
G
,
E
G
is a bijection
f
:
V
G
⟶
1,2
,
…
,
V
G
such that an edge
e
=
u
v
is assigned the label 1 if
f
u
=
f
v
n
or
f
v
=
f
u
n
, for some
n
∈
N
∪
0
and the label 0 otherwise, and satisfy the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1.
The graph that admits power cordial labeling is called a power cordial graph.
In this paper, we derive some characterizations of power cordial graphs as well as explore NP-complete problems for power cordial labeling.
This work also rules out any possibility of forbidden subgraph characterization for power cordial labeling.
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