Abstract
The irregularity of a graph is the sum of the absolute values of the differences of degrees of pairs of adjacent vertices. In this paper, we obtain an upper bound on the irregularity of graphs in terms of the order, the size and the number of pendant vertices, and characterize the extremal graphs. Moreover, we characterize the graphs with maximum irregularity among all graphs with the given order and the number of pendant vertices. Finally, sharp upper bounds are given on the irregularity of graphs with cut edges.
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Acknowledgements
The author is grateful to the two anonymous referees for their careful reading of this paper and criticisms, constructive corrections and valuable comments on this paper, which have considerably improved the presentation of this paper. K. C. Das is supported by National Research Foundation funded by the Korean government (Grant no. 2021R1F1A1050646).
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Communicated by Carlos Hoppen.
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Dorjsembe, S., Buyantogtokh, L., Das, K.C. et al. Graphs with maximum irregularity. Comp. Appl. Math. 41, 262 (2022). https://doi.org/10.1007/s40314-022-01967-3
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DOI: https://doi.org/10.1007/s40314-022-01967-3