Advances and Applications in Discrete Mathematics
Volume 16, Issue 1, Pages 31 - 40
(July 2015) http://dx.doi.org/10.17654/AADMJul2015_031_040 |
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TOTAL IRREGULARITY STRENGTH OF THE GENERALIZED WEB GRAPH
N. S. Hungund
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Abstract: An edge irregular total k-labeling of a graph G is such a labeling of the vertices and edges with integers that the weights of any two different edges are distinct, where the weight of an edge is the sum of the label of the edge itself and the labels of its incident vertices. The minimum k, for which the graph G has an edge irregular total k-labeling, is called the total edge irregularity strength of the graph G and is denoted by Similarly a vertex irregular total k-labeling of a graph G is such a labeling of the vertices and edges with integers that the weights of any two different vertices are distinct, where the weight of a vertex is the sum of the label of the vertex itself and the labels of its incident edges. The minimum k, for which the graph G has a vertex irregular total k-labeling, is called the total vertex irregularity strength of the graph G and is denoted by
In this paper, we determine the exact value of the total edge irregularity strength and an upper bound of the total vertex irregularity strength of the generalized web graph for |
Keywords and phrases: graphs, an edge irregular total k-labeling, a vertex irregular total k-labeling, the total edge irregularity strength, the total vertex irregularity strength, the web graph the generalized web graph |
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