On Detour Distance Laplacian Energy

V. Kaladevi, A. Abinayaa

Abstract


The Detour distance laplacian energy of a simple connected graph \(G\) is defined as the sum of the absolute values of the Eigen values of the detour distance laplacian matrix of \(G\). In this paper, the bounds for detour distance laplacian energy is obtain and also the detour distance laplacian energy of standard graphs and the Cartesian product of certain graphs with \(P_2\) are computed.

Keywords


Detour distance Laplacian matrix; Detour distance Laplacian Eigen value; Detour distance Laplacian energy

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References


C. Adiga, A. Bayad, I. Gutman and S.A. Srinivas, The minimum coveringenergy 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.

M. Aouchiche and P. Hansen, Two Laplacians for the distance matrix of agraph, 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.

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

S.B. Bozkunt, A.D. Gungor and B. Zhou, Note on the distance energy of graphs, MATCH Commun. Math Comput. Chem. 64 (2010), 129 – 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, in Algebraic Combinatorics and Applications, A. Betten, A. Kobnert, R. Lave and A. Wassermann (eds.), Springer, Berlin (2001), 196 – 211.

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.

B. Zohu and X. Cai, On detour index, MATCH Commun. Math. Comput. Chem. 63 (2010), 199 – 210.




DOI: http://dx.doi.org/10.26713%2Fjims.v9i3.934

eISSN 0975-5748; pISSN 0974-875X