@article{Article_27,

title = {On Rational Clique Roots of Maximal Outerplanar Graphs},

journal = {Communications in Combinatorics, Cryptography & Computer Science},

volume = {2022},

issue = {1},

issn = { 2783-5456 },

year = {2022},

url = {http://cccs.sgh.ac.ir/Articles/2022/issue 1/1-3-OnRationalCliqueRootsofMaximalOuterplanarGraphs.pdf},

author = {Hossein Teimoori Faal},

keywords = {Maximal outerplanar graphs, clique polynomial, triangulated graphs, Apollonian networks, clique roots.},

abstract = {The ordinary generating function of the number of complete subgraphs of a simple graph G is called the clique polynomial of G. A real root of a clique polynomial of a graph G is called a clique root of G. In this paper, we prove that the class of maximal outerplanar garphs has only rational clique roots. In particular, we show that maximal outerplanar graphs have a clique root r=-1 of multiplicity two. We also disuss about some possible extensions of our results to the class of maximal planar graphs. We finally conclude the paper with some interesting open questions and conjectures.}

};