## 147 Citations

On the Nonorientable Genus of the Generalized Unit and Unitary Cayley Graphs of a Commutative Ring

- Mathematics, ArtAlgebra Colloquium
- 2022

Let [Formula: see text] be a commutative ring and [Formula: see text] the multiplicative group of unit elements of [Formula: see text]. In 2012, Khashyarmanesh et al. defined the generalized unit and…

Minor-minimal non-projective planar graphs with an internal 3-separation

- MathematicsElectron. Notes Discret. Math.
- 2011

On possible counterexamples to Negami's planar cover conjecture

- MathematicsJ. Graph Theory
- 2004

It is shown that there are, up to obvious constructions, at most 16 possible counterexamples to Negami's conjecture, and a finite list of sets of graphs such that the set of excluded minors for the property of having finite planar cover is one of the sets in the list.

Another two graphs with no planar covers

- MathematicsJ. Graph Theory
- 2001

It is proved that the graphs C4 and E2 have no planar covers, and it is shown that that there are, up to obvious constructions, at most 16 possible counterexamples to Negami's conjecture.

Power graphs of (non)orientable genus two

- MathematicsCommunications in Algebra
- 2019

Abstract The power graph of a finite group is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other. In this article, we classify the finite…

Classification of Finite Groups with Toroidal or Projective-Planar Permutability Graphs

- Mathematics
- 2015

Let G be a group. The permutability graph of subgroups of G, denoted by Γ(G), is a graph having all the proper subgroups of G as its vertices, and two subgroups are adjacent in Γ(G) if and only if…

Projective Total Graphs of Commutative Rings

- Mathematics
- 2013

Let T (Γ(R)) be the total graph of a commutative ringR, that is, a graph with all elements of R as vertices and two distinct vertices a and b are adjacent if and only if a+ b is a zero-divisor on R.…

The embedding of line graphs associated to the zero-divisor graphs of commutative rings

- Mathematics
- 2010

Let R be a commutative ring with identity and denote Γ(R) for its zero-divisor graph. In this paper, we study the minimal embedding of the line graph associated to Γ(R), denoted by L(Γ(R)), into…

The Regular Excluded Minors for Signed-Graphic Matroids

- MathematicsCombinatorics, Probability and Computing
- 2009

We show that the complete list of regular excluded minors for the class of signed-graphic matroids is M*(G1),. . . , M*(G29), R15, R16. Here G1,. . . , G29 are the vertically 2-connected excluded…

## References

SHOWING 1-7 OF 7 REFERENCES

Graphs with bounded valency that do not embed in the projective plane

- MathematicsDiscret. Math.
- 1977

A Kuratowski theorem for the projective plane

- MathematicsJ. Graph Theory
- 1981

Let I ( S ) denote the set of graphs, each with no valency 2 vertices, which are irreducible for S, and using this notation the authors state Kuratowski's theorem.

Additivity of the genus of a graph

- Mathematics
- 1962

In this note a graph G is a finite 1-complex, and an imbedding of G in an orientable 2-manifold M is a geometric realization of G in M. The letter G will also be used to designate the set in M which…