- Title
- On the total irregularity strength of cycles and paths
- Creator
- Marzuki, C. C.; Salman, A. N. M.; Miller, M.
- Relation
- Far East Journal of Mathematical Sciences Vol. 82, Issue 1, p. 1-21
- Relation
- http://www.pphmj.com/journals/fjms.htm
- Publisher
- Pushpa Publishing House
- Resource Type
- journal article
- Date
- 2013
- Description
- The vertex irregular total labeling and the edge irregular total labeling were introduced by Bača et al. Combining both of these notions, in this paper, we introduce a new irregular total labeling, called 'totally irregular total labeling' which is required to be both vertex and edge irregular. Let G = (V, E) be a graph. A function f : V∪E → {1, 2, ..., k} of a graph G is a totally irregular total k-labeling if for any two different vertices x and y of G, their weights wt(x) and wt(y) are distinct and for any two different edges x1x2 and y1y2 of G, their weights wt(x1x2) and wt(y1y2) are distinct, where the weight wt(x) of a vertex x is the sum of the label of x and the labels of all edges incident with x, and the weight wt(x1x2) of an edge x1x2 is the sum of the label of edge x1x2 and the labels of vertices x1 and x2. The minimum k for which a graph G has a totally irregular total k-labeling is called the total irregularity strength of G, denoted by ts(G). In this paper, we provide an upper bound and a lower bound of the total irregularity strength of a graph. Besides that, we determine the total irregularity strength of cycles and paths.
- Identifier
- http://hdl.handle.net/1959.13/1342806
- Identifier
- uon:29034
- Identifier
- ISSN:0972-0871
- Language
- eng
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