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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. |
URI: | http://dyuthi.cusat.ac.in/purl/615 |
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vijaya kumar maths.pdf | (231.6Kb) |
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. |
URI: | http://dyuthi.cusat.ac.in/purl/627 |
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A_Note_on_energy_of_some_graphs.pdf | (324.8Kb) |
Abstract: | The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D, and the D-energy ED(G) is the sum of the absolute values of its D-eigenvalues. Two graphs are said to be D-equienergetic if they have the same D-energy. In this note we obtain bounds for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular D-equienergetic graphs of diameter 2, on p = 3t + 1 vertices are also constructed. |
URI: | http://dyuthi.cusat.ac.in/purl/1537 |
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On distance energy of graphs.PDF | (2.514Mb) |
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