### Outer independent square free detour number of a graph

#### Abstract

For a connected graph , a set of vertices is called an outer independent square free detour set if is a square free detour set of such that either* * or is an independent set. The minimum cardinality of an outer independent square free detour set of is called an outer independent square free detour number of and is denoted by We determine the outer independent square free detour number of some graphs. We characterize the graph which realizes the result that for any pair of integers and* * with there exists a connected graph of order with square free detour number and outer independent square free detour number

#### Keywords

#### Full Text:

PDF#### References

Asir, I. Keerthi, and S. Athisayanathan. Triangle free detour distance in graphs. J. Combin. Math. Combin. Comput 105 (2016).

Chartrand, Gary, Garry L. Johns, and Songlin Tian. Detour distance in graphs. Annals of discrete mathematics. Vol. 55. Elsevier (1993): 127-136.

Chartrand, Garry L. Johns and Ping Zhang. The detour number of a graph. Util. Math. 64, (2003): 97-113.

Christy Rani K. and Priscilla Pacifica G. Square free detour number of some derived graphs. Proceedings of International conference on recent trends in mathematics and its applications (2022): 978-93-5680-181-3: 48-52.

Jalaei, R., and D. A. Mojdeh. Outer independent double Italian domination: Complexity, characterization. Discrete Mathematics, Algorithms and Applications (2022): 2250085.

John, J., and N. Ariyanayagam. The detour domination number of a graph. Discrete mathematics, algorithms and applications 9.01 (2017): 149-170.

Santhakumaran, A. P., and S. Athisayanathan. On the connected detour number of a graph. Journal of Prime research in Mathematics 5 (2009): 149-170.

Sethu Ramalingam, S., and S. Athisayanathan. Upper triangle free detour number of a graph. Discrete Mathematics, Algorithms and Applications 14.01 (2022): 2150094.

DOI: http://dx.doi.org/10.23755/rm.v44i0.919

### Refbacks

- There are currently no refbacks.

Copyright (c) 2022 K Christy Rani, G Pricilla Pacifica

This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.