Open Access
2016 On Gated Sets in Graphs
Manoj Changat, Iztok Peterin, Abisha Ramachandran
Taiwanese J. Math. 20(3): 509-521 (2016). DOI: 10.11650/tjm.20.2016.6422
Abstract

A subset $K$ of vertices of a graph $G$ is gated if for every vertex $x \in V(G)$ there exists a gate $v \in K$ which is on a shortest path between $x$ and any vertex $u$ of $K$. We give a characterization of gated sets in an arbitrary graph $G$ and several necessary conditions. This characterization yields very nice results in the case of weakly modular graphs, which are also presented. We also show that the trees are precisely the graphs which present a convex geometry with respect to the gated convexity.

Copyright © 2016 The Mathematical Society of the Republic of China
Manoj Changat, Iztok Peterin, and Abisha Ramachandran "On Gated Sets in Graphs," Taiwanese Journal of Mathematics 20(3), 509-521, (2016). https://doi.org/10.11650/tjm.20.2016.6422
Published: 2016
Vol.20 • No. 3 • 2016
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