Perfect codes in direct graph bundles

Ladinek, Irena Hrastnik; Žerovnik, Janez

doi:10.1016/j.ipl.2015.03.010

Cited by 2 publications

(2 citation statements)

References 13 publications

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“…In the last period, the study of perfect codes in graphs was primarily focused on their existence and construction in some central families of graphs. Many researches were done on standard graph products and product-like graphs [2,23,28,39,42,44]. Among other classes of graphs on which perfect codes were investigated we mention Sierpiński graphs [8,27], cubic vertex-transitive graphs [31], circulant graphs [10], twisted tori [24], dual cubes [25], and AT-free and dually chordal graphs [4].…”

Section: Introductionmentioning

confidence: 99%

Graphs that are simultaneously efficient open domination and efficient closed domination graphs

Klavžar

Peterin

Yero

2017

Discrete Applied Mathematics

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A graph is an efficient open (resp. closed) domination graph if there exists a subset of vertices whose open (resp. closed) neighborhoods partition its vertex set. Graphs that are efficient open as well as efficient closed (shortly EOCD graphs) are investigated. The structure of EOCD graphs with respect to their efficient open and efficient closed dominating sets is explained. It is shown that the decision problem regarding whether a graph is an EOCD graph is an NP-complete problem. A recursive description that constructs all EOCD trees is given and EOCD graphs are characterized among the Sierpiński graphs.

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Section: Introductionmentioning

confidence: 99%

Graphs that are simultaneously efficient open domination and efficient closed domination graphs

Klavžar

Peterin

Yero

2017

Discrete Applied Mathematics

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“…Classes of graphs similar to products for which perfect codes were investigated include direct graph bundles [9] and twisted tori [12]. Perfect codes were also investigated in other classes of graphs, notably on Sierpiński graphs [5,14], Cayley graphs [6], cubic vertex-transitive graphs [18], circulant graphs [7,20], and AT-free and dually chordal graphs [4].…”

Section: Introductionmentioning

confidence: 99%