Abstract
A λ-labelling of graph G is an integer labelling of V( G) such that adjacent vertices have labels that differ by at least two and vertices distance two apart have labels that differ by at least one. The λ number of G, λ( G), is the minimum span of labels over all such labellings. Griggs and Yeh have studied the relationship between λ( G) and graph invariants χ( G) and Δ ( G). In this paper, we derive the relationship between λ( G) and another graph invariant, the path covering number of G c . Applications include the determination of the λ-number of the join of two graphs, the product of two complete graphs, and the complete multi-partite graphs.
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