Abstract
In this paper, we introduce a new matrix for a graph G in which i th row sum and i th column sum are both equal to neighbors degree sum of i th vertex and define a new variant of graph energy called neighbors degree sum energy \(E_{N} (G)\) of a graph G. The striking feature of this new matrix is that it is related with some well known degree based topological indices like Zagreb type indices, forgotten indices, etc. When \(E_N(G)\) values of some molecules containing hetero atoms are correlated with their total \(\pi \)–electron energy, we got a good correlation with the correlation coefficient \(r=0.982\). \(E_N(G)\) values of some selected 25 polyaromatic hydrocarbons also showed excellent correlation with their \(\pi \)–electron energy values with the correlation coefficient \(r=0.997\). Further, we computed neighbors degree sum energy of some standard classes of graphs and established some bounds and characterizations on largest eigenvalue of N(G) and neighbors degree sum energy of graphs.
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Acknowledgements
The author Boregowda H. S. is thankful to Tumkur University for support through research Grant under TU: D.E.V: IQAC-II(4237): 2019-20/60(1), Dated 02/04/2019. Both the authors thank anonymous reviewers for their careful reading of the manuscript, insightful comments and valuable suggestions.
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Boregowda, H.S., Jummannaver, R.B. Neighbors degree sum energy of graphs. J. Appl. Math. Comput. 67, 579–603 (2021). https://doi.org/10.1007/s12190-020-01480-y
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DOI: https://doi.org/10.1007/s12190-020-01480-y