Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

We add a fixed number of vertices of degree 1 to each vertex from one part of a bipartite graph. We study characteristic, matching and some related polynomials for graphs obtained in this way.

We derive a formula for the chromatic polynomial of a chordal or a triangulated graph in terms of its maximal cliques. As a corollary we obtain a way to write down an explicit formula for the ...