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Wang, Long; Fang, Xianwen; Geng, Xianya
Discrete mathematics, 20/May , Letnik: 345, Številka: 5Journal Article
Let G be a connected graph with n(G) vertices and e(G) edges. The nullity of G, denoted by η(G), is the multiplicity of eigenvalue zero of the adjacency matrix of G. Ma, Wong and Tian (2016) proved that η(G)≤2c(G)+p(G)−1 unless G is a cycle of order a multiple of 4, where c(G)=e(G)−n(G)+1 is the elementary cyclic number of G and p(G) is the number of leaves of G. Recently, Chang, Chang and Zheng (2020) characterized the leaf-free graphs with nullity 2c(G)−1, thus leaving the problem to characterize connected graphs G with nullity2c(G)+p(G)−1whenp(G)≠0. In this paper, we solve this problem completely.
