Acta Mathematica Sinica, English Series

, Volume 34, Issue 5, pp 911–920 | Cite as

On the Characterization of Maximal Planar Graphs with a Given Signed Cycle Domination Number

  • Xiao Ming Pi


Let G = (V, E) be a simple graph. A function f : E → {+1,−1} is called a signed cycle domination function (SCDF) of G if ƩeE(C)f(e) ≥ 1 for every induced cycle C of G. The signed cycle domination number of G is defined as γsc(G) = min{ƩeEf(e)| f is an SCDF of G}. This paper will characterize all maximal planar graphs G with order n ≥ 6 and γsc(G) = n.


Domination number signed cycle domination function signed cycle domination number planar graph maximal planar graph 

MR(2010) Subject Classification



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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Normal UniversityHarbinP. R. China

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