Displaying similar documents to “Algebraic properties of edge ideals via combinatorial topology.”

Extremely Irregular Graphs

M. Tavakoli, F. Rahbarnia, M. Mirzavaziri, A. R. Ashrafi, I. Gutman (2013)

Kragujevac Journal of Mathematics

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On 3-simplicial vertices in planar graphs

Endre Boros, Robert E. Jamison, Renu Laskar, Henry Martyn Mulder (2004)

Discussiones Mathematicae Graph Theory

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A vertex v in a graph G = (V,E) is k-simplicial if the neighborhood N(v) of v can be vertex-covered by k or fewer complete graphs. The main result of the paper states that a planar graph of order at least four has at least four 3-simplicial vertices of degree at most five. This result is a strengthening of the classical corollary of Euler's Formula that a planar graph of order at least four contains at least four vertices of degree at most five.

Gallai and anti-Gallai graphs of a graph

Aparna Lakshmanan S., S. B. Rao, A. Vijayakumar (2007)

Mathematica Bohemica

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The paper deals with graph operators—the Gallai graphs and the anti-Gallai graphs. We prove the existence of a finite family of forbidden subgraphs for the Gallai graphs and the anti-Gallai graphs to be H -free for any finite graph H . The case of complement reducible graphs—cographs is discussed in detail. Some relations between the chromatic number, the radius and the diameter of a graph and its Gallai and anti-Gallai graphs are also obtained.