@article{Adiyanyam2022, 
author = {Damchaa Adiyanyam and Enkhbayar Azjargal and Lkhagva Buyantogtokh},
title = {Bond incident degree indices of stepwise irregular graphs},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {5},
pages = {8685-8700},
keywords = {maximum degree, stepwise irregular graph, BID index, bipartite graph},
url = {https://www.sciopen.com/article/10.3934/math.2022485},
doi = {10.3934/math.2022485},
abstract = {The bond incident degree (BID) index of a graph    G is defined as    B  I      D          f        (  G  )  =      ∑          u      v      ∈      E      (      G      )        f  (  d  (  u  )  ,  d  (  v  )  ), where    d  (  u  ) is the degree of a vertex    u and    f is a non-negative real valued symmetric function of two variables. A graph is stepwise irregular if the degrees of any two of its adjacent vertices differ by exactly one. In this paper, we give a sharp upper bound on the maximum degree of stepwise irregular graphs of order    n when    n  ≡  2  (            m      o      d          4  ), and we give upper bounds on    B  I      D          f       index in terms of the order    n and the maximum degree    Δ. Moreover, we completely characterize the extremal stepwise irregular graphs of order    n with respect to    B  I      D          f      .}
}