| Summary: | The beta-number of a graph G is the smallest positive integer n for which there exists an injective function f : V G → 0 , 1 , … , n such that each u v ∈ E G is labeled | f u − f v | and the resulting set of edge labels is c , c + 1 , … , c + | E G | − 1 for some positive integer c. The beta-number of G is + ∞, otherwise. If c = 1, then the resulting beta-number is called the strong beta-number of G. A linear forest is a forest for which each component is a path. In this paper, we determine a formula for the (strong) beta-number of the linear forests with two components. This leads us to a partial formula for the beta-number of the disjoint union of multiple copies of the same linear forests. Keywords: Beta-number, Strong beta-number, Gracefulness, Graceful labeling, Linear forest
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