IJPAM: Volume 113, No. 3 (2017)

Title

SOME NEW SUM PERFECT SQUARE GRAPHS

Authors

S.G. Sonchhatra$^1$, G.V. Ghodasara$^2$
$^{1}$School of Science
R.K. University
Rajkot, INDIA
$^1$Government Engineering College
Rajkot, Gujarat, INDIA
$^2$H. H.B. Kotak Institute of Science
Rajkot, Gujarat, INDIA

Abstract

A $(p,q)$ graph $G = (V, E)$ is called sum perfect square if for a bijection $f:V(G)\rightarrow\{0,1,2,\ldots, p-1\}$ there exists an injection $f^{\ast}:E(G)\rightarrow\mathbb{N}$ defined by $f^{\ast}(uv)=(f(u))^{2} + (f(v))^{2} + 2 f(u) \cdot f(v)$, $\forall uv \in E(G)$. Here $f$ is called sum perfect square labeling of $G$. In this paper we derive several new sum perfect square graphs.

History

Received: December 28, 2016
Revised: February 20, 2017
Published: March 28, 2017

AMS Classification, Key Words

AMS Subject Classification: 05C78.
Key Words and Phrases: Sum perfect square graph, half wheel graph

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Bibliography

1
F. Harary, Graph Theory, Addision-wesley, Reading, MA, (1969).

2
J.A. Gallian, A dynemic survey of graph labeling, The Electronics Journal of Combinatorics, 18 (2015) 1-262.

3
J. Shiama, Square sum labeling for some middle and total graphs, International Journal of Computer Applications, 37 (2012) 6-8, doi: https://doi.org/10.5120/4594-6548.

4
S.G. Sonchhatra, G.V. Ghodasara, Sum perfect square labeling of graphs, International Journal of Scientific and Innovative Mathematical Research, 4 (2016) 64-70.

How to Cite?

DOI: 10.12732/ijpam.v113i3.11 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: 2017
Volume: 113
Issue: 3
Pages: 489 - 499


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