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The list Distinguishing Number Equals the Distinguishing Number for Interval Graphs

100%

Immel P., Wenger P. S.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 1

165-174

A distinguishing coloring of a graph G is a coloring of the vertices so that every nontrivial automorphism of G maps some vertex to a vertex with a different color. The distinguishing number of G is the minimum k such that G has a distinguishing coloring where each vertex is assigned a color from {1, . . . , k}. A list assignment to G is an assignment L = {L(v)}v∈V (G) of lists of colors to the vertices of G. A distinguishing L-coloring of G is a distinguishing coloring of G where the color of each vertex v comes from L(v). The list distinguishing number of G is the minimum k such that every list assignment to G in which |L(v)| = k for all v ∈ V (G) yields a distinguishing L-coloring of G. We prove that if G is an interval graph, then its distinguishing number and list distinguishing number are equal.

Sierpiński graphs as spanning subgraphs of Hanoi graphs

100%

Hinz A., Klavžar S., Zemljič S.

Open Mathematics

2013

tom 11

nr 6

1153-1157

Hanoi graphs H pn model the Tower of Hanoi game with p pegs and n discs. Sierpinski graphs S pn arose in investigations of universal topological spaces and have meanwhile been studied extensively. It is proved that S pn embeds as a spanning subgraph into H pn if and only if p is odd or, trivially, if n = 1.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Open Mathematics

1 Hinz A.

1 Immel P.

1 Klavžar S.

1 Wenger P. S.

1 Zemljič S.

1 2017

1 2013

Wyniki wyszukiwania

The list Distinguishing Number Equals the Distinguishing Number for Interval Graphs

Sierpiński graphs as spanning subgraphs of Hanoi graphs