Graph polynomials and paintability of plane graphs

Some Graph Polynomials of the Power Graph and its Supergraphs

‎In this paper‎, ‎exact formulas for the dependence‎, ‎independence‎, ‎vertex cover and clique polynomials of the power graph and its‎ ‎supergraphs for certain finite groups are presented‎.

Sum-Paintability of Generalized Theta-Graphs

In online list coloring (introduced by Zhu and by Schauz in 2009), on each round the set of vertices having a particular color in their lists is revealed, and the coloring algorithm chooses an independent subset of this set to receive that color. For a graph G and a function f : V (G) → N, the graph is f -paintable if there is an algorithm to produce a proper coloring when each vertex v is allo...

The Polynomials of a Graph

In this paper, we are presented a formula for the polynomial of a graph. Our main result is the following formula: [Sum (d{_u}(k))]=[Sum (a{_kj}{S{_G}^j}(1))], where, u is an element of V(G) and 1<=j<=k.

Tutte Polynomials of Flower Graphs

Counting Plane Graphs: Cross-Graph Charging Schemes

We study cross-graph charging schemes for graphs drawn in the plane. These are charging schemes where charge is moved across vertices of different graphs. Such methods have been recently applied to obtain various properties of triangulations that are embedded over a fixed set of points in the plane. We show how this method can be generalized to obtain results for various other types of graphs t...