Six signed Petersen graphs, and their automorphisms

  title={Six signed Petersen graphs, and their automorphisms},
  author={Thomas Zaslavsky},
  journal={Discret. Math.},

Concerning Some Properties of Signed Graphs Associated With Specific Graphs

Two signed graphs are called switching isomorphic if one of them is isomorphic to a switching equivalent of the other. To determine the number of switching non-isomorphic signed graphs on a specific

The chromatic polynomials of signed Petersen graphs

Zaslavsky proved in 2012 that, up to switching isomorphism, there are six different signed Petersen graphs and that they could be told apart by their chromatic polynomials, by showing that the latter

Computing the Chromatic Polynomials of the Six Signed Petersen Graphs

Graphs are a collection of vertices and edges that connect some vertices to others. Signed graphs are graphs whose edges are assigned positive or negative labels and may contain loops. Signed graphs

Signed Complete Graphs on Six Vertices

A signed graph is a graph whose edges are labeled positive or negative. The sign of a cycle is the product of the signs of its edges. Zaslavsky proved in 2012 that, up to switching isomorphism, there

Some Topics concerning Graphs, Signed Graphs and Matroids

We discuss well-quasi-ordering in graphs and signed graphs, giving two short proofs of the bounded case of S. B. Rao’s conjecture. We give a characterization of graphs whose bicircular matroids are

Signed Chromatic Polynomials of Signed Book Graphs

In 2015, Matthias Beck and his team developed a computer program in SAGE which efficiently determines the number of signed proper $k$-colorings for a given signed graph. In this article, we determine

Non-isomorphic signatures on some generalised Petersen graph

In this paper we find the number of different signatures of $P(3,1), P(5,1)$ and $P(7,1)$ upto switching isomorphism, where $P(n, k)$ denotes the generalised Petersen graph, $2k < n$. We also count

Enumeration of Switching Non-isomorphic Signed Wheels

Two signed graphs are called switching isomorphic to each other if one is isomorphic to a switching of the other. The wheel Wn is the join of the cycle Cn and a vertex. For 0 ≤ p ≤ n, ψp(n) is

Frustration in signed graphs

Zaslavsky conjectured the following: The minimum number of vertices to be deleted to restore balance in a subcubic signed graph is the same as the minimum number of edges to be deleted to restore



Computer generation of edge groups and edge colorings of graphs

A computer code and nonnumerical algorithm are developed to construct the edge group of a graph and to enumerate the edge colorings of graphs of chemical interest. The edge colorings of graphs have

Chromatic invariants of signed graphs

Algebraic Graph Theory

The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.

Algebraic Graph Theory

1. Introduction to algebraic graph theory Part I. Linear Algebra in Graphic Thoery: 2. The spectrum of a graph 3. Regular graphs and line graphs 4. Cycles and cuts 5. Spanning trees and associated

Signed graph coloring

Characterizations of signed graphs

Two characterizations are given here of the possible classes of balanced circles of a signed graph: an elementary one of the balanced portion of an arbitrary subclass of circles, and a strongerOne of the entire balanced circle class.

The Petersen graph

1. The Petersen graph 2. The four colour problem 3. Snarks 4. Factors 5. Beyond the four colour theorem 6. Cages 7. Hypohamiltonian graphs 8. Symmetry 9. The Petersen graph in diversity Index.

Morphology of ground states of two-dimensional frustration model

The problem of generating ground states of a quenched random Ising spin system with variable concentration of mixed-neighbour exchange couplings (Jij()0) on a planar lattice (frustration model) is

On the measurement of structural balance

If in a group of people every one loves his friends' friends and also his enemies' enemies and hates his friends' enemies and his enemies' friends, the “signed graph” representing the network of