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A Reduction of the Graph Reconstruction Conjecture

100%

Monikandan S., Balakumar J.

Discussiones Mathematicae Graph Theory

2014

tom 34

nr 3

529-537

A graph is said to be reconstructible if it is determined up to isomor- phism from the collection of all its one-vertex deleted unlabeled subgraphs. Reconstruction Conjecture (RC) asserts that all graphs on at least three vertices are reconstructible. In this paper, we prove that interval-regular graphs and some new classes of graphs are reconstructible and show that RC is true if and only if all non-geodetic and non-interval-regular blocks G with diam(G) = 2 or diam(Ḡ) = diam(G) = 3 are reconstructible

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The edge C₄ graph of some graph classes

88%

Menon M., Vijayakumar A.

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 3

365-375

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, there exists a super graph H such that C(H) = G and C(E₄(H)) = E₄(G). Also we give forbidden subgraph characterizations for E₄(G) being a threshold graph, block graph, geodetic graph and weakly geodetic graph.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Balakumar J.

1 Menon M.

1 Monikandan S.

1 Vijayakumar A.

1 2014

1 2010

Wyniki wyszukiwania

A Reduction of the Graph Reconstruction Conjecture

The edge C₄ graph of some graph classes