On the maximum size of stepwise irregular graphs

Lkhagva Buyantogtokh, Enkhbayar Azjargal, Batmend Horoldagva, Shiikhar Dorjsembe and Damchaa Adiyanyam

Applied Mathematics and Computation, 2021, vol. 392, issue C

Abstract: Recently, Gutman introduced the class of stepwise irregular graphs and studied their properties. A graph is stepwise irregular if the difference between the degrees of any two adjacent vertices is exactly one. In this paper, we get some upper bounds on the maximum degree and sharp upper bounds on the size of stepwise irregular graphs. Furthermore, we completely characterize the graphs with maximum size among all connected stepwise irregular graphs of the given order.

Keywords: Irregularity; Maximum degree; Stepwise irregular graph; Bipartite graph (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320306366

DOI: 10.1016/j.amc.2020.125683

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