All Connected Graphs with Maximum Degree at Most 3 whose Energies are Equal to the Number of Vertices
نویسندگان
چکیده
The energy E(G) of a graph G is defined as the sum of the absolute values of its eigenvalues. Let S2 be the star of order 2 (or K2) and Q be the graph obtained from S2 by attaching two pendent edges to each of the end vertices of S2. Majstorović et al. conjectured that S2, Q and the complete bipartite graphs K2,2 and K3,3 are the only 4 connected graphs with maximum degree ∆ ≤ 3 whose energies are equal to the number of vertices. This paper is devoted to giving a confirmative proof to the conjecture.
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