关键词: 邻接矩阵, 奇异图, 零度, 概率

Abstract: By using the method that the determinant of the adjacency matrix of the singular graph was equal to zero, we discussed the singularity of the generalized θ-graphs and the generalized plum blossom φ-graphs, and gave the necessary and sufficient conditions for the generalized θ-graph θ(a₁,a₂,…,a_k) and the generalized plum blossom graph φ(a₁,a₂,…,a_k) to be a singular graph, respectively. The probability values of singular graph occurring in these two types of graphs were calculated.

Key words: adjacency matrix, singular graph, nullity, probability