Radio number for the product of a path and a complete graph

Byeong Moon Kim (), Woonjae Hwang () and Byung Chul Song ()
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Byeong Moon Kim: Gangneung-Wonju National University
Woonjae Hwang: Korea University
Byung Chul Song: Gangneung-Wonju National University

Journal of Combinatorial Optimization, 2015, vol. 30, issue 1, No 11, 139-149

Abstract: Abstract A multilevel distance labeling of a graph $$G=(V,E)$$ G = ( V , E ) is a function $$f$$ f on $$V$$ V into $$\mathbb N \cup \{0\}$$ N ∪ { 0 } such that $$|f(v)-f(w)| \ge \text{ diam }(G)+1-\text{ dist }(v,w)$$ | f ( v ) - f ( w ) | ≥ diam ( G ) + 1 - dist ( v , w ) for all $$v,w\in V$$ v , w ∈ V . The radio number $$\text{ rn }(G)$$ rn ( G ) of $$G$$ G is the minimum span over all multilevel distance labelings of $$G$$ G . In this paper, we completely determine the radio number $$\text{ rn }(G)$$ rn ( G ) of $$G$$ G where $$G$$ G is the Cartesian product of a path $$P_n$$ P n with $$n\,(n\ge 4)$$ n ( n ≥ 4 ) vertices and a complete graph $$K_m$$ K m with $$m\,(m\ge 3)$$ m ( m ≥ 3 ) vertices.

Keywords: Multilevel distance labeling; Channel assignment problem; Radio number; Cartesian product; 05c78; 05c15; 05c12 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-013-9639-3

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