We show that if G is a connected graph with the same proper convex subgraphs as (Kn)', the Cartesian product of r copies of Kn, r >t 2, n >t 3, then [V(G)I ~> n" with equality if and only if G is isomorphic to (Kn)'. In this note we consider only connected finite undirected simple graphs. The compl
โฆ LIBER โฆ
Convex domination in the composition and cartesian product of graphs
โ Scribed by Labendia, Mhelmar A.; Canoy, Sergio R.
- Book ID
- 118797808
- Publisher
- Springer
- Year
- 2012
- Tongue
- English
- Weight
- 102 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0011-4642
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## Abstract This article proves the following result: Let __G__ and __G__โฒ be graphs of orders __n__ and __n__โฒ, respectively. Let __G__^\*^ be obtained from __G__ by adding to each vertex a set of __n__โฒ degree 1 neighbors. If __G__^\*^ has game coloring number __m__ and __G__โฒ has acyclic chromat
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