Let G be a simple connected graph with vertex set V(G) and edge set E(G). Suppose N represents a network derived from G by substituting a 1-ohm resistor for each edge of G. In that case, the resistance between \(u, v \in V(G)\) is analogous to the resistance between two equivalent nodes in network N. The Kirchhoff index of G is the summation of the resistance distances between all pairs of vertices in G. The line graph \(L_G\) of G is a graph whose vertices correspond to the edges of G, and any two vertices of \(L_G\) are adjacent if and only if the corresponding edges of G are incident with the same vertex of G. A unicyclic graph is a connected graph containing exactly one cycle. In this paper, we will identify the extremal values and unicyclic graphs for the Kirchhoff index of the line graph of unicyclic graphs by utilizing techniques derived from electrical networks.
