Monophonic Distance Energy for Join of Some Graphs

V S Sinju Manohar, T Binu Selin

Abstract


Let G be a connected graph with n vertices and m edges. Let µ1, µ2 ,..., µn be the Eigen values of distance matrix of G. The distance energy of a graph ED (G) = \sum_{i=1}^{p}\left|{\mu_i}^\ \right|,was already studied. We now define and investigate the monophonic distance energy as EM (G) = \sum_{i=1}^{n}\left|{\mu_i}^M\right|, where µ1M, µ2M..., µnM are the eigen values of monophonic distance matrix of graphs. In this paper we find the monophonic distance energy for join of some graphs.

Keywords


Join; Monophonic distance energy.

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References


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

I. Gutman, The energy of a graph, Ber. Math-Statist. Sekt. Forschungsz.Graz, 103, 1-22, 1978.

F. Harary, Graph Theory, Addison-Wesley, Boston,1969.

G. Indulal, I. Gutman and A. Vijayakumar, On Distance energy of a Graph, MATCH commun. Math. Comput. Chem (2008),461-472.

G. Indulal and A. Vijayakumar, On a pair of Equienergetic Graphs, MATCH commun. Math. Comput. chem (2008), 83-90.

G. Indulal and I. Gutman, On the distance spectra of some graphs, Mathematical communications 13(2008), 123-131.

Samir K. Vaidya and Kalpesh M. Popat, Some new results on energy of Graphs, MATCH commun. Math. Comput. chem(2017), 589-594.

A. P. Santhakumaran, P. Titus and K. Ganesamoorthy, On the Monophonic number of a graph, J. Appl. Math. and informatics Vol.32(2014), no.1-2, pp.255-266.




DOI: http://dx.doi.org/10.23755/rm.v45i0.979

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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.