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- W436739755 abstract "An identifying code in a graph is a dominating set that also has the property that the closed neighborhood of each vertex in the graph has a distinct intersection with the set. The minimum cardinality of an identifying code in a graph G is denoted γ(G). We consider identifying codes of the direct product Kn × Km. In particular, we answer a question of Klavžar and show the exact value of γ(Kn×Km). It was recently shown by Gravier, Moncel and Semri that for the Cartesian product of two same-sized cliques γ(Kn Kn) = b 3n 2 c. Letting m ≥ n ≥ 2 be any integers, we show that γ(Kn Km) = max{2m − n,m + bn/2c}. Furthermore, we improve upon the bounds for γ(G Km) and explore the specific case when G is the Cartesian product of multiple cliques. Given two disjoint copies of a graph G, denoted G and G, and a permutation π of V (G), the permutation graph πG is constructed by joining u ∈ V (G) to π(u) ∈ V (G) for all u ∈ V (G). The graph G is said to be a universal fixer if the domination number of πG is equal to the domination number of G for all π of V (G). In 1999 it was conjectured that the only universal fixers are the edgeless graphs. We prove the conjecture." @default.
- W436739755 created "2016-06-24" @default.
- W436739755 creator A5018001470 @default.
- W436739755 date "2014-01-01" @default.
- W436739755 modified "2023-09-27" @default.
- W436739755 title "Identifying codes and domination in the product of graphs" @default.
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