MINIMUM DOMINATING DISTANCE ENERGY OF A GRAPH

rajesh kanna, DHARMENDRA B N, SRIDHARA G

Abstract


Recently we introduced the concept of minimum dominating energy[21]. Motivatedby this paper,we introduced the concept of minimum dominating distance energyEDd(G) of a graph G and computed minimum dominating distance energies of a Stargraph,Complete graph,Crown graph and Cocktail graphs. Upper and lower boundsfor EDd(G) are also established.

DOI : http://dx.doi.org/10.22342/jims.20.1.133.19-29


Keywords


Minimum dominating set, Minimum dominating distance matrix, Minimum dominating distance eigenvalues, Minimum dominating distance energy of a graph. 1 I

Full Text:

PDF

References


R.B.Bapat, page No.32,Graphs and Matrices,Hindustan Book Agency,(2011).

R.B.Bapat, S.Pati, Energy of a graph is never an odd integer.Bull. Kerala Math.

Assoc. 1, 129 - 132 (2011)

S. B. Bozkurt, A. D. Gungor, B. Zhou, Note on the distance energy of graphs,

MATCH Commun. Math. Comput. Chem. 64 (2010) 129134.

G. Caporossi, E. Chasset, B. Furtula, Some conjectures and properties on distance

energy, Les Cahiers du GERAD G-2009-64 (2009) V+17.

D.Cvetkovic, I.Gutman (eds.),Applications of Graph Spectra (Mathematical Institution,

Belgrade,2009)

D. Cvetkovic, I.Gutman (eds.) Selected Topics on Applications of Graph Spectra,

(Mathematical Institute Belgrade,2011)

A.Graovac, I.Gutman, N.Trinajstic,Topological Approach to the Chemistry of

Conjugated Molecules (Springer, Berlin,1977)

A. D. Gungor, S. B. Bozkurt, On the distance spectral radius and distance energy

of graphs, Lin. Multilin. Algebra 59 (2011) 365370.

I.Gutman,The energy of a graph.Ber. Math-Statist. Sekt. Forschungsz.Graz 103,

-22 (1978)

I.Gutman, X. Li, J.Zhang,in Graph Energy,ed. by M.Dehmer, F.Emmert - Streib.

Analysis of Complex Networks. From Biology to Linguistics (Wiley - VCH, Weinheim,

,pp. 145 174.

I.Gutman, in The energy of a graph: Old and New Results,ed.by A. Betten,

A. Kohnert, R. Laue, A. Wassermann. Algebraic Combinatorics and Applications

(Springer, Berlin,2001),pp. 196 - 211.

I.Gutman, O.E. Polansky,Mathematical Concepts in Organic Chemistry

(Springer, Berlin,1986)

Huiqing Liu,Mei Lu and Feng Tian,Some upper bounds for the energy of graphs

Journal of Mathematical Chemistry, Vol. 41, No.1, (2007).

A. Ilic, Distance spectra and distance energy of integral circulant graphs, Lin.

Algebra Appl. 433 (2010) 10051014.

G. Indulal, Sharp bounds on the distance spectral radius and the distance energy

of graphs, Lin. Algebra Appl. 430 (2009) 106113.

G. Indulal, I. Gutman, A. Vijayakumar, On distance energy of graphs,MATCH

Commun. Math. Comput. Chem. 60 (2008) 461472.

G. Indulal, I. Gutman, D-Equienergetic self-complementary graphs, Kragujevac

J. Math. 32 (2009) 123131.

J.H. Koolen, V. Moulton, Maximal energy graphs. Adv.Appl. Math. 26,47 - 52

(2001)

M. Liu, A note on D-equienergetic graphs, MATCH Commun. Math. Comput.

Chem. 64 (2010) 125140.

B.J.McClelland, Properties of the latent roots of a matrix: The estimation of

-electron energies.J. Chem. Phys.54, 640 - 643 (1971)

M.R.Rajesh Kanna, B. N. Dharmendra, and G. Sridhara, Minimum Dominating

Energy of a Graph. International Journal of Pure and Applied Mathematics, 85,

No. 4 (2013) 707-718.

H. S. Ramane, I. Gutman, D. S. Revankar, Distance equienergetic

graphs,MATCH Commun. Math. Comput. Chem. 60 (2008) 473484.

H. S. Ramane, D. S. Revankar, I. Gutman, S. B. Rao, B. D. Acharya, H. B.

Walikar, Bounds for the distance energy of a graph, Kragujevac J. Math. 31 (2008)

H. S. Ramane, D. S. Revankar, I. Gutman, H. B. Walikar, Distance spectra

and distance energies of iterated line graphs of regular graphs, Publ. Inst. Math.

(Beograd) 85 (2009) 3946.

D. Stevanovic, G. Indulal, The distance spectrum and energy of the composition

of regular graphs, Appl. Math. Lett. 22 (2009) 11361140.

B. Zhou, A. Ilic, On distance spectral radius and distance energy of

graphs,MATCH Commun. Math. Comput. Chem. 64 (2010) 261280.




DOI: https://doi.org/10.22342/jims.20.1.133.19-29

Refbacks

  • There are currently no refbacks.



Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
Senolowo, Sinduadi, Mlati, Sleman Regency, Special Region of Yogyakarta 55281, Telp. (0274) 552243
Email: jims.indoms@gmail.com


p-ISSN: 2086-8952 | e-ISSN: 2460-0245


Journal of the Indonesian Mathematical Society is licensed under a Creative Commons Attribution 4.0 International License

web statistics
View My Stats