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Jie-Hua Mai, Song Shao (2007)
Fundamenta Mathematicae
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Let (X,f) be a dynamical system. In general the set of all ω-limit sets of f is not closed in the hyperspace of closed subsets of X. In this paper we study the case when X is a graph, and show that the family of ω-limit sets of a graph map is closed with respect to the Hausdorff metric.
J. Nieminen (1975)
Applicationes Mathematicae
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Manju K. Menon, A. Vijayakumar (2010)
Discussiones Mathematicae Graph Theory
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The edge C₄ graph of a graph G, E₄(G) is a graph whose vertices are the edges of G and two vertices in E₄(G) are adjacent if the corresponding edges in G are either incident or are opposite edges of some C₄. In this paper, we show that there exist infinitely many pairs of non isomorphic graphs whose edge C₄ graphs are isomorphic. We study the relationship between the diameter, radius and domination number of G and those of E₄(G). It is shown that for any graph G without isolated vertices,...
Ursescu, Corneliu (2005)
International Journal of Mathematics and Mathematical Sciences
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Don R. Lick (1976)
Colloquium Mathematicae
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C. S., Jr. Johnson, Frederick R. McMorris (1982)
Mathematica Slovaca
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D. M. Cvetković (1975)
Matematički Vesnik
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Zaslavsky, Thomas (1998)
The Electronic Journal of Combinatorics [electronic only]
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Susan A. van Aardt (2017)
Discussiones Mathematicae Graph Theory
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A digraph of order n is k-traceable if n ≥ k and each of its induced subdigraphs of order k is traceable. It is known that if 2 ≤ k ≤ 6, every k-traceable oriented graph is traceable but for k = 7 and for each k ≥ 9, there exist k-traceable oriented graphs that are nontraceable. We show that every 8-traceable oriented graph is traceable.
Dragoš M. Cvetković, Irena Pevac (1983)
Publications de l'Institut Mathématique
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Mohammad Hailat (2012)
Discussiones Mathematicae Graph Theory
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The Friendship Theorem states that if any two people, of a group of at least three people, have exactly one friend in common, then there is always a person who is everybody's friend. In this paper, we generalize the Friendship Theorem to the case that in a group of at least three people, if every two friends have one or two common friends and every pair of strangers have exactly one friend then there exist one person who is friend to everybody in the group. In particular, we show that...
Broderick Arneson, Piotr Rudnicki (2006)
Formalized Mathematics
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We are formalizing the algorithm for recognizing chordal graphs by lexicographic breadth-first search as presented in [13, Section 3 of Chapter 4, pp. 81-84]. Then we follow with a formalization of another algorithm serving the same end but based on maximum cardinality search as presented by Tarjan and Yannakakis [25].This work is a part of the MSc work of the first author under supervision of the second author. We would like to thank one of the anonymous reviewers for very useful suggestions. ...