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

Xin Zhang

Applied Mathematics and Computation, 2019, vol. 350, issue C, 163-169

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.

Keywords: q-planar graph; Degree sum; Crossing mumber; first general Zagreb index; General zeroth-order Randić index (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:350:y:2019:i:c:p:163-169

DOI: 10.1016/j.amc.2019.01.002

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