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K-Product
Cordial Labeling
of Powers of
Paths
K. Jeya Daisy (1), R. Santrin Sabibha (2),
P. Jeyanthi
(3) and
Maged Z. Youssef
(4)
(1) Department
of Mathematics,
Holy Cross
College,
Nagercoil,
Tamilnadu, India
Email address:
jeyadaisy@yahoo.com
(2) Research
scholar, Register
no.: 20212072092001,
Manonmaniam
Sundaranar
University,
Tirunelveli,
Tamilnadu, India
Email address:
sanithazhi@gmail.com
(3) Research Centre,
Department of
Mathematics,
Govindammal Aditanar
College for Women,
Tiruchendur 628215,
Tamilnadu, India
Email address:
jeyajeyanthi@rediffmail.com
(4) Department of
Mathematics and
Statistics, College
of Science, Imam
Mohammad Ibn Saud
Islamic University,
Riyadh 11623, Saudi
Arabia. Department
of Mathematics,
Faculty of Science,
Ain Shams
University, Abbassia,
Cairo, Egypt
Email address:
mzyoussef11566@yahoo.com
Doi :
https://doi.org/10.47013/15.4.8
Cited by :
Jordan J. Math &
Stat.,
15 (4A) (2022),
911 - 924
PDF
Received on:
June 8, 2021;
Accepted
on: April 14,
2022
Abstract. Let f be a
map from V (G)
to {0, 1, ..., k
− 1}, where k is
an integer and 1
≤ k ≤ |V (G)|.
For each edge uv
assign the label
f(u)f(v)(mod k).
f is called a
k-product
cordial labeling
if |vf
(i) − vf
(j)| ≤ 1, and |ef
(i) − ef
(j)| ≤ 1, i, j ϵ
{0, 1, ..., k −
1}, where vf
(x) and ef
(x) denote
the number of
vertices and
edges,
respectively
labeled with x
(x = 0, 1, ...,
k − 1). In this
paper, we add
some new results
on k-product
cordial labeling
and prove that
the graph P2n
is 4-product
cordial.
Further, we
study the
k-product
cordial
behaviour of
powers of paths
P3n,
P4n
and P5n
for k = 3 and 4.
Keywords: cordial
labeling,
product cordial
labeling,
k-product
cordial
labeling,
3-product
cordial
labeling,
4-product
cordial
labeling.
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