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 ...

A set of novel vertex-degree-based invariants was introduced by Gutman, denoted by SO₁, SO₂, . . . , SO₆. These invariants were constructed through geometric reasoning based on a new graph invariant ...

A realizable degree sequence can be realized in many ways as a graph. There are several tests for determining realizability of a degree sequence. Up to now, not much was known about the common ...