A survey of the algorithmic properties of simplicial, upper bound and middle graphs.
Cheston, Grant A., Jap, Tjoen Seng (2006)
Journal of Graph Algorithms and Applications
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Cheston, Grant A., Jap, Tjoen Seng (2006)
Journal of Graph Algorithms and Applications
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Gutman, Ivan (1992)
Publications de l'Institut Mathématique. Nouvelle Série
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M. Tavakoli, F. Rahbarnia, M. Mirzavaziri, A. R. Ashrafi, I. Gutman (2013)
Kragujevac Journal of Mathematics
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Nikolopoulos, Stavros D., Palios, Leonidas (2005)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Abbas, N., Culberson, J., Stewart, L. (2005)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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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.
S. Aparna Lakshmanan, 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 -free for any finite graph . 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.
A. K. Dewdney, Frank Harary (1976)
Czechoslovak Mathematical Journal
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Chia, Gek Ling, Ho, Chee-Kit (2003)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Villarreal, Rafael H. (2007)
Revista Colombiana de Matemáticas
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Gutman, I. (1996)
Publications de l'Institut Mathématique. Nouvelle Série
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