A Note on Circular Distance Energy and Circular Distance Laplacian Energy

Authors

  • V. Kaladevi Department of Mathematics, Bishop Heber College, Trichy 17, Tamilnadu
  • R. Bhuvaneshwari Department of Mathematics, Bishop Heber College, Trichy 17, Tamilnadu

DOI:

https://doi.org/10.26713/jims.v9i3.941

Keywords:

Circular distance matrix, Circular distance energy, Circular distance laplacian energy

Abstract

The circular distance energy of a simple connected graph \(G\) is defined as the sum of the absolute values of its eigen values of the circular distance matrix of \(G\). In this paper, the bounds for circular distance energy is obtained. Also the circular distance energy and the circular distance laplacian energy of certain graphs via circular distance energy are derived.

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References

C. Adiga, A. Bayad, I. Gutman and S.A Srinivas, The minimum covering energy of a graph, Kragujevac J. Sci. 34(2012), 39 – 56.

C. Adiga and M. Smitha, On maximum degree energy of a graph, Int. J. Contemp. Math. Sciences 4 (8) (2009), 385 – 396.

V. Kaladevi and P. Selvarani, Detour sum and wiener sum of chain diamond silicate network, Bulletin of Pure and Applied Sciences 31E (Math & Stat.) (1) (2012), 67 – 72.

K.M. Kathiresan, C. Parameswaran, G. Marimuthu and S. Arockiaraj, Detour Wiener Indices of Graphs, Bulletin of the ICA 62 (2011), 33 – 47.

V. Kaladevi and P. Selvarani, Three polynomials in one matrix, Mathematical Sciences International Research Journal 1 (2), 100 – 108.

M. Aouchiche and P. Hansen, Two Laplacians for the distance matrix of a graph, Linear Algebra Appl. 439 (2013), 21 – 33.

S.K. Ayyasamy and S. Balachandran, On detour spectra of some graphs, World Academy of Science, Engineering and Technology 4 (2010), 07 – 21.

Bala krishnan, The energy of a graph, Lin. Algebra Appl. 387 (2004), 287 – 295.

Bozohu and Xiaochum Cai, On detour index, MATCH commun. Math. Comput. Chem. 63 (2010), 199 – 210.

S.B. Bozkunt, A.D. Gungor and B. Zhou, Note on the distance energy of graphs, MATCH Commun. Math Comput. Chem. (2010), 64129 – 134.

F. Buckley and F. Harary, Distance in Graphs, Addison-Wesley, Redwood (1990).

M. Edelberg, M.R. Garey and R.L. Graham, On the distance matrix of a tree, Discr. Math. 14 (1976), 23 – 29.

A.D. Gunger and S.B. Bozkurt, On the distance spectral radius and distance energy of graphs, Lin. Multilin. Algebra 59(2011), 365 – 370.

I. Gutman, The energy of a graph, Ber. Math. Statist.Sekt. for Schungsz. Ghaz. 103 (1978), 1 – 22.

I. Gutman, The Energy of a Graph, Old and New Results (eds.: A. Betten, A. Kobnert, R. Lave and A. Wassermann, Algebraic Combinatorics and Applications, Springer, Berlin, 196 – 211 (2001).

R.L. Graham and L. Lovasz, Distance matrix polynomials of trees, Adv. Math. 29 (1978), 60 – 88.

H. Hua, On minimal energy of unicycle graphs with prescribed girth and pendent vertices, MATCH Commun. Math. Comput. Chem. 57 (2007), 351 – 361.

G. Indulal, Sharp bounds on the distance spectral radius and the distance energy of graphs, Lin. Algebra Appl. 430 (2009), 106 – 113.

G. Indulal, I. Gutman and A. Vijayakumar, On distance energy of graphs, MATCH Commun. Math. Comput. Chem. 60 (2008), 461 – 472.

J. Yang, L. You and I. Gutman, Bounds on the distance laplacian energy of graphs, Kragujevac journal of Mathematics 37 (2) (2013), 245 – 255.

J.H. Koolen and V. Moulton, Maximal Energy Graphs, Adv.Appl. Math. 26 (2001), 47 – 52.

I. Lukovits, The detour index, Croat. Chem. Acta 69 (1996), 873 – 882.

I. Lukovits and M. Razinger, On calculation of the detour index, J. Chem. Inf. Comput. Sci. 37 (1997), 283 – 286.

H.S. Ramane, D.S. Revankar, I. Gutman, S.B. Rao, B.D. Acharya and H.B. Walikar, Bounds for the distance energy of a graph, Kragujevac J. Math. 31 (2008), 59 – 68.

N. Trinajstic, S. Nikolic, B. Lucic, D. Amic and Z. Mihalic, The detour matrix in chemistry, J. Chem. Inf. Comput. Sci. 37 (1997), 631 – 638.

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Published

2017-10-30
CITATION

How to Cite

Kaladevi, V., & Bhuvaneshwari, R. (2017). A Note on Circular Distance Energy and Circular Distance Laplacian Energy. Journal of Informatics and Mathematical Sciences, 9(3), 791–797. https://doi.org/10.26713/jims.v9i3.941

Issue

Vol. 9 No. 3 (2017)

Section

Research Articles

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