Relative clique number of planar signed graphs
Article Type
Research Article
Publication Title
Discrete Applied Mathematics
Abstract
A signed relative clique number of signed graph (where edges are assigned positive or negative signs) is the size of a largest subset X of vertices such that every two vertices are either adjacent or are part of a 4-cycle with an odd number of negative edges. The signed relative clique number is sandwiched between two other parameters of signed graphs, namely, the signed absolute clique number and the signed chromatic number, all three notions defined in Naserasr et al. (2014). Thus, together with a result from Ochem et al. (2016) the lower bound of 8 and upper bound of 40 has already been proved for the signed relative clique number of the family of planar graphs. Here we improve the upper bound to 15. Furthermore, we determine the exact values of signed relative clique number of the families of outerplanar graphs and triangle-free planar graphs.
First Page
86
Last Page
92
DOI
10.1016/j.dam.2018.03.005
Publication Date
6-15-2020
Recommended Citation
Das, Sandip; Ghosh, Prantar; Prabhu, Swathy; and Sen, Sagnik, "Relative clique number of planar signed graphs" (2020). Journal Articles. 245.
https://digitalcommons.isical.ac.in/journal-articles/245