Author(s)

Haicheng Ma^*, Shang Gao, Danyang Li

Department of Mathematics, Qinghai Nationalities University Xining, Qinghai, China.

Let G be a graph of order n with vertex set V(G) = {v₁, v₂,…, v_n}. the adjacency matrix of G is an n × n matrix A(G) = (a_ij)_n×n, where a_ij is the number edges joining v_i and v_j in G. The eigenvalues λ₁, λ₂, λ₃,…, λ_n, of A(G) are said to be the eigenvalues of the graph G and to form the spectrum of this graph. The number of nonzero eigenvalues and zero eigenvalues in the spectrum of G are called rank and nullity of the graph G, and are denoted by r(G) and η(G), respectively. It follows from the definitions that r(G) + η(G) = n. In this paper, by using the operation of multiplication of vertices, a characterization for graph G with pendant vertices and r(G) = 7 is shown, and then a characterization for graph G with pendant vertices and r(G) less than or equal to 7 is shown.

Adjacency Matrix, Rank, Nullity, Multiplication of Vertices

Ma, H. , Gao, S. and Li, D. (2020) Graphs with Pendant Vertices and r(G) ≤ 7. Journal of Applied Mathematics and Physics, 8, 240-246. doi: 10.4236/jamp.2020.82019.