Double quadrilateral snakes on k-odd sequential harmonious labeling of graphs

A. Manonmani; R. Savithiri

doi:10.26637/mjm304/019

Abstract

The objective of this paper is to investigate some $k$-odd sequential harmonious labeling of graphs. In particular, we show that $k$-odd sequential harmonious labeling of double quadrilateral snakes $\left(2 Q_x\right.$-snakes) for each $x \geq 1$. We also prove that, $2 m Q_x$-snakes are $k$-odd sequential harmonious labeling of graphs for each $m, x \geq 1$. Finally, we present some examples and verified to illustrate proposed theories.

Keywords:

Labeling, Harmonious, Double quadrilateral snake, $k$-odd sequential harmonious

Mathematics Subject Classification:

05C78

Authors Imprint References Funding Related Articles Downloads

A. Manonmani Department of Mathematics, LRG Government Arts College for Women, Tirupur-641604, Tamil Nadu, India. https://orcid.org/0009-0000-6084-1416
R. Savithiri Department of Mathematics, LRG Government Arts College for Women, Tirupur-641604, Tamil Nadu, India.

Pages: 607-611
Date Published: 01-10-2015
Vol. 3 No. 04 (2015): Malaya Journal of Matematik (MJM)

] S.K.Vaidya and N.H.Shah, odd sequential harmonious labeling of some graphs - Presented in International Journal of Mathematical sciences, vol.3(2012), 105-112.

] B.Gayathri and V.Hemalatha, On sequential harmonious labeling of graphs, In Proceeding of the International Conference on Mathematics and Computer Science.

] R.Ponraj and S.Sathish Narayanan, Difference cordiality of some graphs obtained from double alternate snake graphs, Global journal of mathematical sciences,5(2013),167-175.

] Z.Liang and Z.Bai, On the odd harmonious graphs with applications, J.Appl. Math. Comput. 29(2009), 105-116. DOI: https://doi.org/10.1007/s12190-008-0101-0

] B.Gayathri and D.Muthuramakrishnan, k-odd sequential harmonious labeling of some graphs.

] S.C.Shee, On harmonious and related graphs, Ars Combin.,23(1987) A,237-247.

] R.Ponraj , S.Sathish Narayanan and R.Kala, Difference cordial labeling of subdivision of snake graphs, Universal journal of Applied mathematics 2(1):40-45,2014. DOI: https://doi.org/10.13189/ujam.2014.020107

] J.Yuan and W.Zhu, Some results on harmonious labeling of graphs, J.Zhengzhou Univ. Nat. Sci. Ed., 30(1998)7-12.

] R.G.Sun, Harmonious and sequential labeling of the book graphs $B_m$, Gaoxiao yingyong shuxue xuebao ser. A, 9(1994)335-337.

] G.S.Singh and T.K.M. Varkey, On odd sequential and bisequential graphs,preprint.

] R.Ponraj , S.Sathish Narayanan and R.Kala Difference cordial labeling of graphs obtained from double snakes, International journal of mathematics research,5,Number3(2013),317-322.