Vol. 24 No. 2 (2025): Mapana Journal of Sciences
Research Articles

BOUNDS ON DISTANCE DIFFERENCE DOMINATING ENERGY OF A GRAPH

  • E LINCY,
  • V MAHESWARI
E LINCY
A.P.C. Mahalaxmi College for Women

Published 2025-08-28

Keywords

  • Eigen values,
  • distance difference dominating matrix,
  • distance difference dominating energy

Copyright (c) 2025

Creative Commons License

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Abstract

This work defines distance difference dominating matrix of graph and estimates characteristic values of distance difference dominating matrix. The summation of absolute eigen/characteristic values of graph's distance difference dominating matrix yields distance difference dominating energy of simple connected graph. The properties of distance difference dominating eigen values are analysed. The boundaries of distance difference dominating energy are established.

References

  1. Biernacki, M., Pidek, H. and Ryll-Nadzewski, C. ,Sur une ine ́galite ́ entre des inte ́grales de ́finies, Univ. Marie CurieUSktoodowska, 1950, A4, 1-4.
  2. Díaz, J.B., & Metcalf, F.T., Stronger forms of a class of inequalities of G. Pólya-G. Szegö, and L. V. Kantorovich., Bulletin of the American Mathematical Society, 1963, 69, 415-418. https://doi.org/10.1090/S0002-9904-1963-10953-2
  3. Dragomir, S.S., A survey on Cauchy-Bunyakovsky-Schwarz type discrete inequalities, JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only] 4.3,2003, 63, 1-142. http://eudml.org/doc/124162
  4. Gutman, I., The Energy of a Graph, Ber. Math-Statist. Sekt. Forschungsz. Graz, 1978, 103, 1-22.
  5. Ozeki, N., On the estimation of the inequalities by the maximum, or minimum values. J. College Arts Sci. Chiba Univ., 1968, 5, 199-203.
  6. Polya, G., Szego, G., Problems and Theorems in Analysis , Series · Integral Calculus·Theory of Functions, Springer New York, 1972. https://doi.org/10.1007/978-1-4757-1640-5
  7. Zakić, Aleksandar & Milovanović, I.Ž & Milovanović, E.I., A Short Note on Graph Energy, MATCH Communications in Mathematical and in Computer Chemistry, 2013, Volume 72, 179-182.