This analysis defines a new matrix and establishes bounds on distance difference dominating energy in graphs.
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.
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Lincy et al. (2025) studied this question.
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