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Currently displaying 1 – 2 of 2

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The edge C₄ graph of some graph classes

Manju K. Menon; A. Vijayakumar — 2010

Discussiones Mathematicae Graph Theory

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...

Containers and wide diameters of $P_{3} (G)$

Daniela Ferrero; Manju K. Menon; A. Vijayakumar — 2012

Mathematica Bohemica

The $P_{3}$ intersection graph of a graph $G$ has for vertices all the induced paths of order 3 in $G$ . Two vertices in $P_{3} (G)$ are adjacent if the corresponding paths in $G$ are not disjoint. A $w$ -container between two different vertices $u$ and $v$ in a graph $G$ is a set of $w$ internally vertex disjoint paths between $u$ and $v$ . The length of a container is the length of the longest path in it. The $w$ -wide diameter of $G$ is the minimum number $l$ such that there is a $w$ -container of length at most $l$ between any pair of different...

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