Mehler formulae for matching polynomials of graphs and independence polynomials of clawfree graphs

Some results on vertex-edge Wiener polynomials and indices of graphs

The vertex-edge Wiener polynomials of a simple connected graph are defined based on the distances between vertices and edges of that graph. The first derivative of these polynomials at one are called the vertex-edge Wiener indices. In this paper, we express some basic properties of the first and second vertex-edge Wiener polynomials of simple connected graphs and compare the first and second ve...

Chromatic Harmonic Indices and Chromatic Harmonic Polynomials of Certain Graphs

In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...

Approximating independence polynomials of claw-free graphs

Matchings in graphs correspond to independent sets in the corresponding line graphs. Line graphs are an important subclass of claw-free graphs. Hence studying independence polynomials of claw-free graphs is a natural extension of studying matching polynomials of graphs. We extend a result of Bayati et.al. showing a fully polynomial time approximation scheme (FPTAS) for computing the independenc...

On Circulants Uniquely Characterized by their Independence Polynomials

In [18], Farrell and Whitehead investigate circulant graphs that are uniquely characterized by their matching and chromatic polynomials (i.e., graphs that are “matching unique” and “chromatic unique”). They develop a partial classification theorem, by finding all matching unique and chromatic unique circulants on n vertices, for each n ≤ 8. In this paper, we explore circulant graphs that are un...

Tutte Polynomials of Flower Graphs