Use this tag for questions in graph theory. Here a graph is a collection of vertices and connecting edges. Use (graphing-functions) instead if your question is about graphing or plotting functions.

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Why graph factorization problems emphasize $k$-regular graphs

When we study graph factorization a lot of emphasis is placed on $k$-factorable graphs, i.e. graphs in which the factors are all $k$-regular. Why is such a factorization more important then say ...
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Is there matrix representation of the line graph operator?

I had the need to calculate the adjacency matrix $L$ of the line graph of a certain planar $k$-regular graphs $G(n,e)$ ( $n$ vertices and $e=\frac k2 n$ edges) given its adjacency matrix $A_G$. Here I ...