Total edge irregularity strength of trees | Zendy

Jaroslav Ivančo | Zendy; Stanislav Jendrol′ | Zendy

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Total edge irregularity strength of trees

Author(s) -

Jaroslav Ivančo,

Stanislav Jendrol′

Publication year - 2006

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1337

Subject(s) - mathematics , combinatorics , enhanced data rates for gsm evolution , artificial intelligence , computer science

A total edge-irregular k-labelling » : V (G) [ E(G) ! f1;2;:::;kg of a graph G is a labelling of vertices and edges of G in such a way that for any difierent 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 ¢ on p vertices tes(T) = maxfd(p + 1)=3e;d(¢ + 1)=2eg:

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