# The edge C₄ graph of some graph classes

Manju K. Menon; A. Vijayakumar

Discussiones Mathematicae Graph Theory (2010)

- Volume: 30, Issue: 3, page 365-375
- ISSN: 2083-5892

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topManju K. Menon, and A. Vijayakumar. "The edge C₄ graph of some graph classes." Discussiones Mathematicae Graph Theory 30.3 (2010): 365-375. <http://eudml.org/doc/270807>.

@article{ManjuK2010,

abstract = {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.},

author = {Manju K. Menon, A. Vijayakumar},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {edge C₄ graph; threshold graph; block graph; geodetic graph; weakly geodetic graph; edge graph},

language = {eng},

number = {3},

pages = {365-375},

title = {The edge C₄ graph of some graph classes},

url = {http://eudml.org/doc/270807},

volume = {30},

year = {2010},

}

TY - JOUR

AU - Manju K. Menon

AU - A. Vijayakumar

TI - The edge C₄ graph of some graph classes

JO - Discussiones Mathematicae Graph Theory

PY - 2010

VL - 30

IS - 3

SP - 365

EP - 375

AB - 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.

LA - eng

KW - edge C₄ graph; threshold graph; block graph; geodetic graph; weakly geodetic graph; edge graph

UR - http://eudml.org/doc/270807

ER -

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