TITLE:
k-Product Cordial Labeling of Path Graphs
AUTHORS:
Robinson Santrin Sabibha, Kruz Jeya Daisy, Pon Jeyanthi, Maged Zakaria Youssef
KEYWORDS:
Cordial Labeling, Product Cordial Labeling, k-Product Cordial Labeling, Path Graph
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.15 No.1,
December
26,
2024
ABSTRACT: In 2012, Ponraj et al. defined a concept of k-product cordial labeling as follows: Let f be a map from
V(
G
)
to
{
0,1,⋯,k−1 }
where k is an integer,
1≤k≤|
V(
G
) |
. For each edge
uv
assign the label
f(
u
)f(
v
)(
modk
)
. f is called a k-product cordial labeling if
|
v
f
(
i
)−
v
f
(
j
) |≤1
, and
|
e
f
(
i
)−
e
f
(
j
) |≤1
,
i,j∈{
0,1,⋯,k−1 }
, where
v
f
(
x
)
and
e
f
(
x
)
denote the number of vertices and edges respectively labeled with x (
x=0,1,⋯,k−1
). Motivated by this concept, we further studied and established that several families of graphs admit k-product cordial labeling. In this paper, we show that the path graphs
P
n
admit k-product cordial labeling.