Connected graphs of genus g with complementary orbits

3 - Chromatic Cubic Graphs with Complementary Connected Domination Number Three

Let G (V, E) be a graph. A subset S of V is called a dominating set of G if every vertex in V-S is adjacent to at least one vertex in S. The domination number γ (G) is the minimum cardinality taken over all such dominating sets in G. A subset S of V is said to be a complementary connected dominating set (ccd-set) if S is a dominating set and < V-S > is connected. The chromatic number χ is the m...

The cyclomatic number of connected graphs without solvable orbits

We study the combinatorics of constructing non-singular geometrically irreducible projective curves that do not admit rational points over finite solvable extensions of the base field. A graph is without solvable orbits if its group of automorphisms acts on each of its orbits through a non-solvable quotient. We prove that there is a connected graph without solvable orbits of cyclomatic number c...

Planar Crossing Numbers of Genus g Graphs

Pach and Tóth [15] proved that any n-vertex graph of genus g and maximum degree d has a planar crossing number at most cdn, for a constant c > 1. We improve on this results by decreasing the bound to O(dgn), if g = o(n), and to O(g), otherwise, and also prove that our result is tight within a constant factor.

A Degree Condition For Graphs to Have Connected (g, f)-Factors

connected graphs cospectral with a friendship graph

let $n$ be any positive integer, the friendship graph $f_n$ consists of $n$ edge-disjoint triangles that all of them meeting in one vertex. a graph $g$ is called cospectral with a graph $h$ if their adjacency matrices have the same eigenvalues. recently in href{http://arxiv.org/pdf/1310.6529v1.pdf}{http://arxiv.org/pdf/1310.6529v1.pdf} it is proved that if $g$ is any graph cospectral with $f_n$...