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- W4220941778 abstract "<abstract><p>The bond incident degree (BID) index of a graph $ G $ is defined as $ BID_{f}(G) = sum_{uvin 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 $ nequiv 2({rm{mod}};4) $, and we give upper bounds on $ BID_{f} $ index in terms of the order $ n $ and the maximum degree $ Delta $. Moreover, we completely characterize the extremal stepwise irregular graphs of order $ n $ with respect to $ BID_{f} $.</p></abstract>" @default.
- W4220941778 created "2022-04-03" @default.
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- W4220941778 date "2022-01-01" @default.
- W4220941778 modified "2023-10-14" @default.
- W4220941778 title "Bond incident degree indices of stepwise irregular graphs" @default.
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- W4220941778 doi "https://doi.org/10.3934/math.2022485" @default.
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