Neighbourly Irregular Derived Graphs

Document Type : Research Paper

Authors

1 KARNATAK UNIVERSITY DHARWAD

2 Karnatak University

3 Ferdowsi University of Mashhad

4 University of Kashan

Abstract

A connected graph G is said to be neighbourly irregular graph if no two adjacent vertices of G have same degree. In this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

Keywords

Main Subjects


1. Y. Alavi, G. Chartrand, F. R. K. Chung, P. Erdos, H. L. Graham, O. R.
Oellermann, Highly irregular graphs, J. Graph Theory 11 (1987) 235–249.
2. S. G. Bhragsam, S. K. Ayyaswamy, Neighbourly irregular graphs, Indian J. Pure
Appl. Math. 35(3) (2004) 389–399.
3. T. Došlić, Vertex-weighted Wiener polynomials for composite graphs, Ars Math.
Contemp. 1 (2008) 66–80.
4. F. Harary, Graph Theory, Addison-Wesley Publishing Co. Inc., Reading, Mass.,
1969.
5. Y. Hou, W-C. Shiu, The spectrum of the edge corona of two graphs, Electron. J.
Linear Algebra 20 (2010) 586–594.
6. S. R. Jog, S. P. Hande, I. Gutman, S. B. Bozkurt, Derived graphs of some graphs,
Kragujevac J. Math. 36(2) (2012) 309–314.
7. V. R. Kulli, B. Basavanagoud, On the quasivertex-total graph of a graph, J.
Karnatak Uni. Sci. 42 (1998) 1–7.
8. E. Sampathkumar, S. B. Chikkodimath, Semitotal graphs of a graph-I, J.
Karnatak Uni. Sci. 18 (1973) 274–280.
9. D. V. S. Sastry, B. Syam Prasad Raju, Graph equations for line graphs, total
graphs, middle graphs and quasi-total graphs, Discrete Math. 48 (1984) 113–119.
10. M. Tavakoli, F. Rahbarnia, A. R. Ashrafi, Studying the corona product of graphs
under some graph invariants, Trans. Comb. 3(3) (2014) 43–49.
11. Y. N. Yeh, I. Gutman, On the sum of all distances in composite graphs, Discrete
Math. 135 (1994) 359–365.
12. H. B. Walikar, S. B. Halkarni, H. S. Ramane, M. Tavakoli, A. R. Ashrafi, On
neighbourly irregular graphs, Kragujevac J. Math. 39(1) (2015) 31–39.