The spanning tree packing number of a graph GG, denoted by τ (G) τ(G), is the maximum
number of edge‐disjoint spanning trees contained in G G. The study of τ (G) τ(G) is one of …

A graph is called $ d $-rigid if there exists a generic embedding of its vertex set into
$\mathbb {R}^ d $ such that every continuous motion of the vertices that preserves the …

A recent result of Cioab\u {a}, Dewar and Gu implies that any $ k $-regular Ramanujan
graph with $ k\geq 8$ is globally rigid in $\mathbb {R}^ 2$. In this paper, we extend these …

Liu, Hong, Gu, and Lai proved if the second largest eigenvalue of the adjacency matrix of
graph $ G $ with minimum degree $\delta\ge 2m+ 2\ge 4$ satisfies $\lambda_2 (G)<\delta …

An $(a, b) $-biregular bipartite graph is a bipartite graph with bipartition $(X, Y) $ such that
each vertex in $ X $ has degree $ a $ and each vertex in $ Y $ has degree $ b $. By the …

Rigidity is the property of a structure that does not flex under an applied force. In the past
several decades, the rigidity of graphs has been widely studied in discrete geometry and …

This work establishes properties of the normalized rigidity matrix in two-and three-
dimensional spaces. The upper bound of the normalized rigidity matrix singular values is …

Over the past half century, the rigidity of graphs in $ R^ 2$ has aroused a great deal of
interest. Lov\'{a} sz and Yemini (1982) proved that every $6 $-connected graph is rigid in …