E-resources
Peer reviewed
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Kim, Byeong Moon; Rho, Yoomi; Song, Byung Chul
Journal of combinatorial optimization, 10/2015, Volume: 30, Issue: 3Journal Article
An L ( j , k ) -labeling of a graph is a vertex labeling such that the difference of the labels of any two adjacent vertices is at least j and that of any two vertices of distance 2 is at least k . The minimum span of all L ( j , k ) -labelings of G is denoted by λ k j ( G ) . Lin and Lam (Discret Math 308:3805–3815, 2008 ) provided an upper bound of λ 1 2 ( K m × C n ) when K m × C n is the direct product of a complete graph K m and a cycle C n . And they found the exact value of λ 1 2 ( K m × C n ) for some m and n . In this paper, we obtain an upper bound and a lower bound of λ 1 1 ( K m × C n ) . As a consequence we compute λ 1 1 ( K m × C n ) when n is even or n ≥ 4 m + 1 .
