Total edge irregularity strength of some cycle related graphs
<p>An edge irregular total <em>k</em>-labeling <em>f</em> : <em>V</em> ∪ <em>E</em> → 1,2, ..., <em>k</em> of a graph <em>G</em> = (<em>V,E</em>) is a labeling of vertices and edges of <em>G</em> in such a way that for any two different edges <em>uv</em> and <em>u'v'</em>, their weights <em>f</em>(<em>u</em>)+<em>f</em>(<em>uv</em>)+<em>f</em>(<em>v</em>) and <em>f</em>(<em>u'</em>)+<em>f</em>(<em>u'v'</em>)+<em>f</em>(<em>v'</em>) are distinct. The total edge irregularity strength tes(<em>G</em>) is defined as the minimum <em>k</em> for which the graph <em>G</em> has an edge irregular total <em>k</em>-labeling. In this paper, we determine the total edge irregularity strength of new classes of graphs <em>C<sub>m</sub></em> @ <em>C<sub>n</sub></em>, <em>P<sub>m,n</sub></em>* and <em>C<sub>m,n</sub></em>* and hence we extend the validity of the conjecture tes(<em>G</em>) = max {⌈|<em>E</em>(<em>G</em>)|+2)/3⌉, ⌈(Δ(<em>G</em>)+1)/2⌉}<em> </em> for some more graphs.</p>
