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Coloring the square of products of cycles and paths
Mahmoodian, E. S ; Sharif University of Technology | 2011
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- Type of Document: Article
- Publisher: 2011
- Abstract:
- The square G2 of a graph G is a graph with the same vertex set as G in which two vertices are joined by an edge if their distance in G is at most two. For a graph G, χ[G2), which is also known as the distance two coloring number of G is studied. We study coloring the square of grids Pm□Pn, cylinders Pm□C n, and tori Cm□Cn. For each m and n we determine χ((Pm□Pn)2), χ(P m□Cn)2), and in some cases χ((C m□Cn)2) while giving sharp bounds to the latter. We show that χ((Cm□Cn)2) is at most 8 except when m -n = 3, in which case the value is 9. Moreover, we conjecture that for every m (m ≥ 5) and n (n ≥ 5), we have, 5 ≤ χ((Cm□Cn)2) ≤ 7
- Keywords:
- Cylinders and tori ; Distance coloring ; Graph G ; Grids ; Sharp bounds ; Vertex set ; Cylinders (shapes) ; Coloring
- Source: Journal of Combinatorial Mathematics and Combinatorial Computing ; Volume 76 , 2011 , Pages 101-119 ; 08353026 (ISSN)
- URL: http://sina.sharif.edu/~emahmood/papers/MR2761017.pdf