Minimum Equitable Dominating Partition Energy of a Graph

Sashi Kanth Reddy Avula, P. Siva Kota Reddy, K. N. Prakasha


The partition energy of a graph was introduced by Sampathkumar et al. [12]. Motivated by this, we introduce the concept of minimum equitable dominating partition energy of a graph, \(E^E_p (G)\) and compute the minimum equitable dominating partition energy \(E^E_p (G)\) of few families of graphs. Also, we establish the bounds for minimum equitable dominating partition energy.


Minimum equitable dominating set; Minimum equitable dominating \(k\)-partition eigenvalues; Minimum equitable dominating k-partition energy; k-Complement; \(k(i)\)-Complement

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

C. Adiga and C.S. Shivakumaraswamy, Bounds on the largest minimum degree eigenvalues of graphs, Int. Math. Forum 5 (37) (2010), 1823 – 1831.

C. Adiga, R. Balakrishnan and W. So, The skew energy of a digraph, Linear Algebra Appl. 432 (2010), 1825 – 1835.

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

C. Adiga, E. Sampathkumar, M.A. Sriraj and A.S. Shrikanth, Color energy of a graph, Proceedings of the Jangjeon Math. Soc. 16 (3) (2013), 335 – 351.

D.M. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs - Theory and Application, Academic Press, New York (1980).

P.J. Davis, Circulant Matrices, Wiley, New York (1979).

H.J. Finck and G. Grohmann, Vollständiges Produkt, chromatische Zahl and charakteristisches Polynom reglärer Graphen, II. Wiss. Z. TH Ilmenau 11 (1965), 81 – 87.

I. Gutman, The energy of a graph, Ber. Math. Stat. Sekt. Forschungsz. Graz 103 (1978), 1 – 22.

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

M.R. Rajesh Kanna, B.N. Dharmendra and G. Sridhara, Minimum dominating energy of a graph, Int. J. Pure Appl. Math. 85 (4) (2013), 707 – 718.

E. Sampathkumar, L. Pushpalatha and C.V. Venkatachalam, P. Bhat, Generalized complements of a graph, Indian J. Pure Appl. Math. 29 (6) (1998), 625 – 639.

E. Sampathkumar, S.V. Roopa, K.A. Vidya and M.A. Sriraj, Partition energy of a graph, Proceedings of the Jangjeon Math. Soc. 16 (3) (2013), 335 – 351.

E. Sampathkumar and M.A. Sriraj, Vertex labeled/colored graphs, matrices and signed Graphs, J. Comb. Inf. Syst. Sci. 38 (2014), 113 – 120.

B. Zhou and I. Gutman, On Laplacian energy of graphs, Match Commun. Math. Comput. Chem. 57 (2007), 211 – 220.


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