IJPAM: Volume 93, No. 4 (2014)

HARMONIOUS AND VERTEX GRACEFUL LABELING
ON PATH AND STAR RELATED GRAPHS

P. Selvaraju$^1$, P. Balaganesan$^2$, J. Renuka$^3$, M.L. Suresh$^4$
$^1$Department of Mathematics
Vel Tech. Multi Tech. Dr. Rangarajan Dr. Sankanthula
Engineering College
Avadi, Chennai, 600 062, INDIA
$^{2,4}$Department of Mathematics
Hindustan University
Chennai, 603 103, INDIA
$^3$Departments of Mathematics
Sri Sai Ram Engineering College
INDIA


Abstract. In this paper, we show that $B^2(n, n)$ is harmonious [4] , $P_i^n$ is harmonious [3], $P_n \times C_m$ is vertex graceful for $ n \geq 2$, and $m \geq 5, m$ is odd, $B^2(n, n)$ is vertex graceful [4] , $P_i^n$ is vertex graceful, [3], $L_n \circ K_1$ is vertex graceful $\forall n$ and $P_n \times P_2$ is vertex graceful, $n$ is odd [3].

Received: October 23, 2013

AMS Subject Classification: 05C78

Key Words and Phrases: harmonious graphs, harmonious labeling, vertex graceful graphs, vertex graceful labeling, bi-stars, path, Cartesian product

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DOI: 10.12732/ijpam.v93i4.2 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 93
Issue: 4
Pages: 501 - 509

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).