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Tricyclic graphs with exactly two main eigenvalues
Main eigenvalues Tricyclic graphs 2-walk (a, b)-linear graphs
2011/1/18
An eigenvalue of a graph G is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, all connected tricyclic graphs with exactly two main eigen...
Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth
Laplacian matrix Laplacian spectral radius girth unicyclic graph
2011/1/18
In this paper we consider the following problem: Over the class of all simple con-nected unicyclic graphs on n vertices with girth g (n, g being fixed), which graph minimizes the Laplacian spectral ra...
In this paper we study zero-divisor graphs of semirings. We show that all zero-divisor graphs of (possibly noncommutative) semirings are connected and have diameter less than or equal to 3. We charact...
Depth of edge rings arising from finite graphs
edge ring toric ideal finite graph Gr¨obner basis initial ideal
2010/12/1
Let G be a finite graph and K[G] the edge ring of G. Based on the technique of Gr¨obner bases and initial ideals, it will be proved that, given integers f and d with 7 f d, there exists a finite g...