Six signed Petersen graphs, and their automorphisms

Six signed Petersen graphs, and their automorphisms

2010 Mathematics Subject Classifications: Primary 05C22; Secondary 05C15, 05C25, 05C30 Abstract. Up to switching isomorphism there are six ways to put signs on the edges of the Petersen graph. We prove this by computing switching invariants, especially frustration indices and frustration numbers, switching automorphism groups, chromatic numbers, and numbers of proper 1-colorations, thereby illu...

Girth six cubic graphs have Petersen minors

We prove that every 3-regular graph with no circuit of length less than six has a subgraph isomorphic to a subdivision of the Petersen graph. 3 January 1997 Revised 17 March 2014 ∗ Research partially performed under a consulting agreement with Bellcore, and partially supported by DIMACS Center, Rutgers University, New Brunswick, New Jersey 08903, USA. 1 Partially supported by NSF under Grant No...

PETERSEN SIGNED GRAPHS PARTIAL DRAFT June 8 , 2009

Symplectic graphs and their automorphisms

The general symplectic graph Sp(2ν, q) is introduced. It is shown that Sp(2ν, q) is strongly regular. Its parameters are computed, its chromatic number and group of graph automorphisms are also determined.

SIGNED GENERALIZED PETERSEN GRAPH AND ITS CHARACTERISTIC POLYNOMIAL

Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefficients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.