Graphs of 20 edges are 2–apex, hence unknotted

Chromaticity of Turan Graphs with At Most Three Edges Deleted

Let $P(G,lambda)$ be the chromatic polynomial of a graph $G$. A graph $G$ ischromatically unique if for any graph $H$, $P(H, lambda) = P(G,lambda)$ implies $H$ is isomorphic to $G$. In this paper, we determine the chromaticity of all Tur'{a}n graphs with at most three edges deleted. As a by product, we found many families of chromatically unique graphs and chromatic equivalence classes of graph...

Visualizing Weighted Edges in Graphs

This paper introduces a new edge length heuristic that finds a graph layout where the edge lengths are proportional to the weights on the graph edges. The heuristic can be used in combination with the spring embedder to produce a compromise between a drawing with an accurate presentation of edge length and a drawing with good general comprehensibility. We describe our preliminary investigations...

Graceful graphs with pendant edges

Graphs with coloring redundant edges

A graph edge is d-coloring redundant if the removal of the edge does not change the set of dcolorings of the graph. Graphs that are too sparse or too dense do not have coloring redundant edges. Tight upper and lower bounds on the number of edges in a graph in order for the graph to have a coloring redundant edge are proven. Two constructions link the class of graphs with a coloring redundant ed...

Disjoint Edges in Topological Graphs

A topological graph G is a graph drawn in the plane so that its edges are represented by Jordan arcs. G is called simple, if any two edges have at most one point in common. It is shown that the maximum number of edges of a simple topological graph with n vertices and no k pairwise disjoint edges is O (