Characterizations of derived graphs
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In this paper, the derived graph of a graph G has the edges of G as its vertices, with adjacency determined by the adjacencies of the edges in G, and a new characterization of derived graphs is given in terms of nine excluded subgraphs.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1970-09-01 and is currently open access. It has received 270 citations till now. The article focuses on the topics: Graph energy & Line graph.read more
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Graph Coloring Problems
Tommy R. Jensen,Bjarne Toft +1 more
TL;DR: In this article, the Conjectures of Hadwiger and Hajos are used to define graph types, such as planar graph, graph on higher surfaces, and critical graph.
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Claw-free graphs—a survey
TL;DR: This paper summarizes known results on claw-free graphs on n ⩽ 12 vertices and investigates the role of independence, domination, and other invariants in hamiltonicity.
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A revision of Minty's algorithm for finding a maximum weight stable set of a claw-free graph
Daishin Nakamura,Akihisa Tamura +1 more
TL;DR: In this paper, it was shown that the algorithm for the weighted version fails for some special cases, and gave modi cations to overcome it, and furthermore, it has been shown that this problem can be solved in polynomial time for many classes of graphs.
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Locally checkable proofs in distributed computing
Mika Göös,Jukka Suomela +1 more
TL;DR: In this work, graph properties are classified according to their local proof complexity, i.
References
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Book ChapterDOI
Congruent Graphs and the Connectivity of Graphs
TL;DR: In this paper, the authors give conditions that two graphs be congruent and some theorems on the connectivity of graphs, and conclude with some applications to dual graphs, which can also be proved by topological methods.
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The interchange graph of a finite graph
TL;DR: In this article, the question of when G' can be isomorphic to G, and how to describe the sequence of iterated interchange graphs of a given G was raised, assuming that G has no loops and no multiple edges.
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On the Uniqueness of the Triangular Association Scheme
TL;DR: In this article, it was shown that the relation among the parameters of the triangular association scheme themselves imply the scheme if $n = 7, but that it is false if n = 8.
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The Uniqueness of the Triangular Association Scheme
TL;DR: In this paper, the question of whether or not these parameters imply the triangular association scheme was addressed, and the answer was shown that they do not imply the triangle association scheme for partially balanced incomplete blocks with two associate classes.