Total Colorings of Some Join Graphs

In this paper, we investigate the total colorings of the join graph \(G_1 + G_2\) where \(G_1 \cup G_2\) is a graph with maximum degree at most \(2\). As a consequence of the main result, we prove that if \(G = (2l+1)C_m + (2l+1)C_n\), then \(G\) is Type 2 if and only if \(m = n\) and \(n\) is odd, where \((2l+1)C_m\) and \((2l+1)C_n\) represent \((2l+1)\) disjoint copies of \(C_m\) and \(C_n\), respectively.