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<p>In computer science, graphs are used in variety of applications directly or indirectly. Especially quantitative labeled graphs have played a vital role in computational linguistics, decision making software tools, coding theory and path determination in networks. For a graph <span class="math"><em>G</em>(<em>V</em>, <em>E</em>)</span> with the vertex set <span class="math"><em>V</em></span> and the edge set <span class="math"><em>E</em></span>, a vertex <span class="math"><em>k</em></span>-labeling <span class="math"><em>ϕ</em> : <em>V</em> → {1, 2, …, <em>k</em>}</span> is defined to be an edge irregular <span class="math"><em>k</em></span>-labeling of the graph <span class="math"><em>G</em></span> if for every two different edges <span class="math"><em>e</em></span> and <span class="math"><em>f</em></span> their <span class="math"><em>w</em>_<em>ϕ</em>(<em>e</em>) ≠ <em>w</em>_<em>ϕ</em>(<em>f</em>)</span>, where the weight of an edge <span class="math"><em>e</em> = <em>x</em><em>y</em> ∈ <em>E</em>(<em>G</em>)</span> is <span class="math"><em>w</em>_<em>ϕ</em>(<em>x</em><em>y</em>) = <em>ϕ</em>(<em>x</em>) + <em>ϕ</em>(<em>y</em>)</span>. The minimum <span class="math"><em>k</em></span> for which the graph <span class="math"><em>G</em></span> has an edge irregular <span class="math"><em>k</em></span>-labeling is called the edge irregularity strength of <span class="math"><em>G</em></span>, denoted by <span class="math"><em>e</em><em>s</em>(<em>G</em>)</span>. In this paper, we determine the edge irregularity strengths of some chain graphs and the join of two graphs. We introduce a conjecture and open problems for researchers for further research.</p>