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The edge C₄ graph of some graph classes

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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.

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1 Discussiones Mathematicae Graph Theory

1 Menon M.

1 Vijayakumar A.

1 2010

Wyniki wyszukiwania

The edge C₄ graph of some graph classes