Indulal,G; Vijayakumar,A(Department of Mathematics, 2008)

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Abstract:

Eigenvalue of a graph is the eigenvalue of its adjacency matrix. The energy of a graph is the
sum of the absolute values of its eigenvalues. In this note we obtain analytic expressions for the
energy of two classes of regular graphs.

Aparna,Lakshmanan S; Vijayakumar,A(Department of Mathematics, 2008)

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Abstract:

In this paper, two notions, the clique irreducibility and clique vertex
irreducibility are discussed. A graph G is clique irreducible if every
clique in G of size at least two, has an edge which does not lie in any
other clique of G and it is clique vertex irreducible if every clique in G
has a vertex which does not lie in any other clique of G. It is proved
that L(G) is clique irreducible if and only if every triangle in G has a
vertex of degree two. The conditions for the iterations of line graph,
the Gallai graphs, the anti-Gallai graphs and its iterations to be clique
irreducible and clique vertex irreducible are also obtained.