query: Proving that irreducibility of a matrix implies strong connectedness of the graph
positive_passages.docid: 145194
positive_passages.text: Matrix graph and irreducibility
negative_passages.docid: 7626
negative_passages.text: Proving that every connected graph has a vertex whose removal will not disconnect the graph.
negative_passages.docid: 6429
negative_passages.text: prove that a connected graph with $n$ vertices has at least $n-1$ edges
negative_passages.docid: 156671
negative_passages.text: Necessary and sufficient condition for $x^n - y^m$ to be irreducible in $\Bbb C[x,y]$
negative_passages.docid: 146933
negative_passages.text: Proving bipartition in a connected planar graph
negative_passages.docid: 94639
negative_passages.text: Proof that the rank of a skew-symmetric matrix is at least $2$
negative_passages.docid: 93304
negative_passages.text: How to prove Graph with $n$ vertices has Edge Chromatic Number no more than $n/2$ edges
negative_passages.docid: 77697
negative_passages.text: Motivation for spectral graph theory.
negative_passages.docid: 26251
negative_passages.text: Prove self-complementarity of regular graph with given order.
negative_passages.docid: 57930
negative_passages.text: Chromatic polynomial properties
negative_passages.docid: 84654
negative_passages.text: The graph of xy = 1 is connected or not
negative_passages.docid: 105996
negative_passages.text: Topology of matrices
negative_passages.docid: 72417
negative_passages.text: Bipartite graphs
negative_passages.docid: 155259
negative_passages.text: Textbook on Graph Theory using Linear Algebra
negative_passages.docid: 35959
negative_passages.text: irreducibility of a polynomial over $\mathbb{F}_2$
negative_passages.docid: 19807
negative_passages.text: Connected graph with colored edges
negative_passages.docid: 39455
negative_passages.text: Prove that $(X\times Y)\setminus (A\times B)$ is connected