The status of a vertex x in a graph is the sum of the distances between x and all other vertices. Let G be a connected graph.Lin posed the following two conjectures. Conjecture 1: A tree and a nontree graph cannot have the same status sequence. Conjecture 2: Any status injective tree is status unique in all connected graphs. We settle these two conjectures negatively.For every integer n ≥ 10, we construct a tree T n and a unicyclic graph U n , both of order n, with the following two properties: (1) T n and U n have the same status sequence; (2) for n ≥ 15, if n is congruent to 3 modulo 4 then T n is status injective and among any four consecutive even orders, there is at least one order n such that T n is status injective.
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