Resistance distance in connected balanced digraphs

Let D be a connected balanced digraph. The classical distance dijD from vertex i to j is the length of shortest directed path in D. L Laplacian matrix and L†=(lij†) Moore–Penrose inverse L. resistance rijD then defined by rijD≔lii†+ljj†−2lij†. C collection digraphs, each member which finite union form D1∪D2∪....∪Dk where Dt digraph with Dt∩(D1∪D2∪⋯∪Dt−1) being single vertex, for all 1<t≤k. In this paper, we show that any C, rijD≤dijD(∗) i,j. This established partitioning suitably. generalizes main result Balaji et al. (2020), namely, inequality (*) holds cactus Related studies have been made many authors. For instance, Gurvich (2022) Vyalyi (2012), Vladimir applied results on digraphs semi-conductors electrical networks. Young (2016) [12,13] , authors study ‘effective distance’ graphs while Chebotarev (2011), graph geodetic studied.