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The adjacency matroid of a graph
adjacency delta-matroid interlace polynomial local complement matroid minor Tutte polynomial
2011/9/22
Abstract: If $G$ is a looped graph, then its adjacency matrix represents a binary matroid $M_{A}(G)$ on $V(G)$. $M_{A}(G)$ may be obtained from the delta-matroid represented by the adjacency matrix of...
Spectral distributions of adjacency and Laplacian matrices of random graphs
Spectral distributions Laplacian matrices random graphs
2010/11/18
In this paper, we investigate the spectral properties of the adjacency and the Laplacian matrices of random graphs. We prove that: (i) the law of large numbers for the spectral norms and the largest ...
Adjacency Preserving Bijection Maps of Hermitian Matrices over any Division Ring with an Involution
division ring with involution hermitian matrix adjacency geometry of matrices
2007/12/11
Let $D$ be any division ring with an involution, ${\mathscr H}_n(D)$ be the space of all $n\times n$ hermitian matrices over $D$. Two hermitian matrices $A$ and $B$ are said to be adjacent if ${\rm ra...