2022
DOI: 10.26493/1855-3974.2496.07a
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The adjacency dimension of graphs

Abstract: It is known that the problem of computing the adjacency dimension of a graph is NPhard. This suggests finding the adjacency dimension for special classes of graphs or obtaining good bounds on this invariant. In this work we obtain general bounds on the adjacency dimension of a graph G in terms of known parameters of G. We discuss the tightness of these bounds and, for some particular classes of graphs, we obtain closed formulae. In particular, we show the close relationships that exist between the adjacency di… Show more

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Cited by 1 publication
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“…Furthermore, Chartrand et al [11] showed that, for any connected graph G, g(G) ≤ n − diam(G) + 1, where dim(G) = max{d(u, v) : u, v ∈ V}. Several researchers have studied this topic and presented some results [12][13][14][15][16][17][18].…”
Section: Introductionmentioning
confidence: 99%
“…Furthermore, Chartrand et al [11] showed that, for any connected graph G, g(G) ≤ n − diam(G) + 1, where dim(G) = max{d(u, v) : u, v ∈ V}. Several researchers have studied this topic and presented some results [12][13][14][15][16][17][18].…”
Section: Introductionmentioning
confidence: 99%