TOTAL VERTEX IRREGULARITY STRENGTH OF TREES WITH MAXIMUM DEGREE FOUR
Baca et al. (2007) introduced the concept of total vertex irregularity labeling. A total vertex irregular k-labeling of G is defined as a mapping from the vertex and edge of G to f1;2; : : : ;kg such that each vertex of G has a distinct weight. The weight of a vertex x 2 V is the sum of the label...
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| Format: | Theses |
| Language: | Indonesia |
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| Online Access: | https://digilib.itb.ac.id/gdl/view/33794 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Baca et al. (2007) introduced the concept of total vertex irregularity labeling. A
total vertex irregular k-labeling of G is defined as a mapping from the vertex and
edge of G to f1;2; : : : ;kg such that each vertex of G has a distinct weight. The
weight of a vertex x 2 V is the sum of the label of x and the labels of all edges
incident to x. The total vertex irregularity strength of G, denoted by tvs(G), is the
smallest positive integer k such that G has a total vertex irregular k-labeling.
Some results on tvs(G) have been obtained for several classes of graphs G. For instance,
Nurdin, Baskoro, Salman and Gaos determined the total vertex irregularity
strength of paths, trees without vertices of degree 2 and 3, quadtrees and banana
trees. They conjectured that the total vertex irregularity strength of any tree is only
determined by the number of vertices of degree 1, 2, and 3. Precisely, they conjectured
this formula:
tvs(T) = maksft1; t2; t3g
where ti = d(1 + åi
j=1 ni)=(i + 1)e and ni is the number of vertices of degree
i 2 [1;3]. In this thesis, we verify this conjecture by considering all trees with
maximum degree four and subdivision of some trees. |
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