A new graph parameter and a construction of larger graph without increasing radio k-chromatic number

Ushnish Sarkar () and Avishek Adhikari ()
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Ushnish Sarkar: University of Calcutta
Avishek Adhikari: University of Calcutta

Journal of Combinatorial Optimization, 2017, vol. 33, issue 4, No 12, 1365-1377

Abstract: Abstract For a positive integer $$k\ge 2$$ k ≥ 2 , the radio k-coloring problem is an assignment L of non-negative integers (colors) to the vertices of a finite simple graph G satisfying the condition $$|L(u)-L(v)| \ge k+1-d(u,v)$$ | L ( u ) - L ( v ) | ≥ k + 1 - d ( u , v ) , for any two distinct vertices u, v of G and d(u, v) being distance between u, v. The span of L is the largest integer assigned by L, while 0 is taken as the smallest color. An $$rc_k$$ r c k -coloring on G is a radio k-coloring on G of minimum span which is referred as the radio k-chromatic number of G and denoted by $$rc_k(G)$$ r c k ( G ) . An integer h, $$0

Keywords: Radio k-coloring; Hole; Maximum degree; Domination number; Path covering number; 05C78; 05C15 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-016-0041-9

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