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Upper bound on the sum of powers of the degrees of graphs with few crossings per edge

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  • Zhang, Xin

Abstract

A graph is q-planar if it can be drawn in the plane so that each edge is crossed by at most q other edges. For fixed integers q ≥ 1 and k ≥ 2, it is proven that 2(n−1)k+o(n) is an asymptotically tight upper bound on the sum of the k-th powers of the degrees of any simple q-planar graph with order n. As a result, an open problem listed at the end of the paper J. Czap, J. Harant, D. Hudák, Discrete Appl. Math. 165 (2014) 146–151 is solved.

Suggested Citation

  • Zhang, Xin, 2019. "Upper bound on the sum of powers of the degrees of graphs with few crossings per edge," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 163-169.
    • Handle: RePEc:eee:apmaco:v:350:y:2019:i:c:p:163-169
    DOI: 10.1016/j.amc.2019.01.002
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    References listed on IDEAS

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    1. Su, Guifu & Tu, Jianhua & Das, Kinkar Ch., 2015. "Graphs with fixed number of pendent vertices and minimal Zeroth-order general Randić index," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 705-710.
    2. Shi, Yongtang, 2015. "Note on two generalizations of the Randić index," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1019-1025.
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