Maximum Total Irregularity of Totally Segregated Extended Bicyclic Graphs

T. F. Jorry

doi:10.26713/cma.v13i3.1818

Authors

T. F. Jorry Department of Mathematics, Mercy College, Palakkad 678006, Kerala, India https://orcid.org/0000-0002-6257-4531 (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v13i3.1818

Keywords:

Total irregularity, Totally segregated graph, Extended bicyclic graph

Abstract

In this paper, we determine maximum total irregularity of two types of connected totally segregated bicyclic graphs on \(n\) vertices: extended \(\infty\) bicyclic graph and \(\Theta\)-bicyclic graph and also characterize those extremal graphs.

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References

H. Abdo, S. Brandt and D. Dimitrov, The total irregularity of a graph, Discrete Mathematics and Theoretical Computer Science 16(1) (2014), 201 – 206, URL: https://dmtcs.episciences.org/1263/pdf.

M. O. Albertson, The irregularity of a graph, Ars Combinatoria 46 (1997), 219 – 225, URL: http://www.combinatoire.ca/ArsCombinatoria/Vol46.html.

F. K. Bell, A note on the irregularity of graphs, Linear Algebra and its Applications 161 (1992), 45 – 54, DOI: 10.1016/0024-3795(92)90004-T.

G. Chartrand, P. Erdös and O. R. Oellermann, How to define an irregular graph, The College Mathematics Journal 19(1) (1988), 36 – 42, DOI: 10.1080/07468342.1988.11973088.

G. H. Fath-Tabar, I. Gutman and R. Nasiri, Extremely irregular trees, Bulletin (Académie serbe des sciences et des arts. Classe des sciences mathématiques et naturelles. Sciences mathématiques) 38 (2013), 1 – 8, URL: https://www.jstor.org/stable/44097193.

I. Gutman, P. Hansen and H. Melot, Variable neighborhood search for extremal graphs. 10. Comparison of irregularity indices for chemical trees, Journal of Chemical Information and Modeling 45(2) (2005), 222 – 230, URL: https://pubs.acs.org/doi/abs/10.1021/ci0342775.

D. E. Jackson and R. Entringer, Totally segregated graphs, Congress. Numer. 55 (1986), 159 – 165.

T. F. Jorry and K. S. Parvathy, Minimum total irregularity of totally segregated ∞-bicyclic graph, International Journal of Recent Technology and Engineering 8(6) (2019), 660 – 663.

L. You, J. Yang, Y. Zhu and Z. You, The maximal total irregularity of bicyclic graphs, Journal of Applied Mathematics 2014 (2014), Article ID 785084, 9 pages, DOI: 10.1155/2014/785084.