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Graph domination in distance two

Gábor Bacsó, Attila Tálos, Zsolt Tuza (2005)

Discussiones Mathematicae Graph Theory

Let G = (V,E) be a graph, and k ≥ 1 an integer. A subgraph D is said to be k-dominating in G if every vertex of G-D is at distance at most k from some vertex of D. For a given class of graphs, Domₖ is the set of those graphs G in which every connected induced subgraph H has some k-dominating induced subgraph D ∈ which is also connected. In our notation, Dom coincides with Dom₁. In this paper we prove that D o m D o m u = D o m u holds for u = all connected graphs without induced P u (u ≥ 2). (In particular, ₂ = K₁ and...

Graph fibrations, graph isomorphism, and PageRank

Paolo Boldi, Violetta Lonati, Massimo Santini, Sebastiano Vigna (2006)

RAIRO - Theoretical Informatics and Applications

PageRank is a ranking method that assigns scores to web pages using the limit distribution of a random walk on the web graph. A fibration of graphs is a morphism that is a local isomorphism of in-neighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. We show that a deep connection relates fibrations and Markov chains with restart, a particular kind of Markov chains that include the PageRank one as a special case. This fact provides constraints on the...

Graph Monoids.

F.W. Roush, K.H. Kim, L.G. Makar-Limanov (1982)

Semigroup forum

Graph operations and neighbor-integrity

Alpay Kırlangıc (2004)

Mathematica Bohemica

Let G be a graph. A vertex subversion strategy of G , say S , is a set of vertices in G whose closed neighborhood is removed from G . The survival-subgraph is denoted by G / S . The Neighbor-Integrity of G , N I ( G ) , is defined to be N I ( G ) = min S V ( G ) { | S | + c ( G / S ) } , where S is any vertex subversion strategy of G , and c ( G / S ) is the maximum order of the components of G / S . In this paper we give some results connecting the neighbor-integrity and binary graph operations.

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