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On total vertex irregularity strength of graphs

100%

Muthu Guru Packiam K., Kathiresan K.

Discussiones Mathematicae Graph Theory

2012

tom 32

nr 1

39-45

Martin Bača et al. [2] introduced the problem of determining the total vertex irregularity strengths of graphs. In this paper we discuss how the addition of new edge affect the total vertex irregularity strength.

Total edge irregularity strength of trees

88%

Ivančo J., Jendrol' S.

Discussiones Mathematicae Graph Theory

2006

tom 26

nr 3

449-456

A total edge-irregular k-labelling ξ:V(G)∪ E(G) → {1,2,...,k} of a graph G is a labelling of vertices and edges of G in such a way that for any different edges e and f their weights wt(e) and wt(f) are distinct. The weight wt(e) of an edge e = xy is the sum of the labels of vertices x and y and the label of the edge e. The minimum k for which a graph G has a total edge-irregular k-labelling is called the total edge irregularity strength of G, tes(G). In this paper we prove that for every tree T of maximum degree Δ on p vertices tes(T) = max{⎡(p+1)/3⎤,⎡(Δ+1)/2⎤}.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Ivančo J.

1 Jendrol' S.

1 Kathiresan K.

1 Muthu Guru Packiam K.

1 2012

1 2006

Wyniki wyszukiwania

On total vertex irregularity strength of graphs

Total edge irregularity strength of trees