The security number of lexicographic products |
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| Authors: | Tanja Gologranc Iztok Peterin |
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| Institution: | 1. University of Maribor, Faculty of Natural Sciences and Mathematics, Koro?ka cesta 160, 2000 Maribor, Slovenia;2. University of Maribor, Faculty of Electrical Engineering and Computer Science, Koro?ka cesta 46, 2000 Maribor, Slovenia |
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| Abstract: | A subset S of vertices of a graph G is a secure set if |N X] ∩ S| ≥ |N X] ? S| holds for any subset X of S, where N X] denotes the closed neighborhood of X. The minimum cardinality s(G) of a secure set in G is called the security number of G. We investigate the security number of lexicographic product graphs by defining a new concept of tightly-securable graphs. In particular we derive several exact results for different families of graphs which yield some general results. |
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| Keywords: | 05C69 05C76 |
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