Displaying similar documents to “On graphs with the largest Laplacian index”

Relations between ( κ , τ ) -regular sets and star complements

Milica Anđelić, Domingos M. Cardoso, Slobodan K. Simić (2013)

Czechoslovak Mathematical Journal

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Let G be a finite graph with an eigenvalue μ of multiplicity m . A set X of m vertices in G is called a star set for μ in G if μ is not an eigenvalue of the star complement G ∖ X which is the subgraph of G induced by vertices not in X . A vertex subset of a graph is ( κ , τ ) -regular if it induces a κ -regular subgraph and every vertex not in the subset has τ neighbors in it. We investigate the graphs having a ( κ , τ ) -regular set which induces a star complement for some eigenvalue. A survey of known results...

Algebraic conditions for t -tough graphs

Bo Lian Liu, Siyuan Chen (2010)

Czechoslovak Mathematical Journal

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We give some algebraic conditions for t -tough graphs in terms of the Laplacian eigenvalues and adjacency eigenvalues of graphs.

Results on F -continuous graphs

Anna Draganova (2009)

Czechoslovak Mathematical Journal

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For any nontrivial connected graph F and any graph G , the of a vertex v in G is the number of copies of F in G containing v . G is called if and only if the F -degrees of any two adjacent vertices in G differ by at most 1; G is if the F -degrees of all vertices in G are the same. This paper classifies all P 4 -continuous graphs with girth greater than 3. We show that for any nontrivial connected graph F other than the star K 1 , k , k ≥ 1 , there exists a regular graph that is not F -continuous. If...