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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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Possible Number of Repetation of a Submatrix
Notation:
$H$ is the adjacency matrix of graph $H'$ respectively. $H_k$ is the block or sub-matrix of matrix $H$. The adjacency matrix of graph $H_k \cup H_e$ (subgraphs of $H'$) is $M_{(k,e)}$ wh …
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Decomposition of a regular graph and connected subgraphs
I have asked almost same question earlier. I have been told that my question was poorly written, so I am trying to write it more clearly in this post. Also, this time I would be a little different in …
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Possibility of Disconnected Subgraphs of a $k$ Connected $r$ regular Graph under a given con...
Context: Given a adjacency matrix A of a $r$-regular graph $G$ (not complete graph $K_{r+1}$) . $G$ is $k$ connected.
The matrix A can be divided into 4 sub-matrices based on adjacency of vertex $x …
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Complexity of reordering a matrix which consists independent sub matrices
Introduction:
Given a matrix A of a $k$ regular graph G. The matrix A can be divided into 4 sub matrices based on adjacency of vertex $x \in G$.
$A_x$ is the symmetric matrix of the graph $(G-x)$, …