Regular ArticleTree Powers
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Cited by (51)
On the two largest distance eigenvalues of graph powers
2017, Information Processing LettersA linear-time algorithm for finding a paired 2-disjoint path cover in the cube of a connected graph
2017, Discrete Applied MathematicsOn pairwise compatibility graphs having Dilworth number two
2014, Theoretical Computer ScienceCitation Excerpt :Nevertheless, researchers interested in computational complexity theory are fascinated by these graphs because the clique problem is known to be polynomially solvable for PCGs once the pairwise compatibility tree is provided [16] (while it is well known that, for a general graph, finding whether there is a clique of a given size is NP-complete [13]). Moreover, the class of PCGs appears interesting by itself from a graph theoretic point of view; nowadays, there are a few results proving that some special classes of graphs are PCGs [1,15,17,19,20] but only two results for general graphs, one affirming that all graphs with a number of nodes not greater than 7 are PCGs [6,18] and the other one proving that not all graphs are PCGs, by means of two graphs that cannot be a PCG, one with 15 nodes [20] and the other one with 8 nodes [11]. The last section proposes some conclusions and open problems arisen from this work.
On pairwise compatibility graphs having Dilworth number k
2014, Theoretical Computer ScienceGraphs with Dilworth Number Two are Pairwise Compatibility Graphs
2013, Electronic Notes in Discrete MathematicsDistance three labelings of trees
2012, Discrete Applied Mathematics
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