Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 4 2026 12 01 Independent location-domination number of graphs 1197 1213 15137 10.22049/cco.2026.30238.2378 EN Pailin Kaewperm Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand Mathematics and Statistics with Applications (MaSA), Bangkok, Thailand David A. Kalarkop Department of Mathematics, St Joseph’s University, Bengaluru, India Pawaton Kaemawichanurat Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand Mathematics and Statistics with Applications (MaSA), Bangkok, Thailand Journal Article 2025 01 01 Let $G = (V(G), E(G))$ be a graph. A set $I \subseteq V(G)$ is independent if no two vertices of $I$ are adjacent. A set $D \subseteq V(G)$ is dominating if every vertex $u \in V(G) \setminus D$ is adjacent to a vertex in $D$. A set $L \subseteq V(G)$ is an independent locating-dominating set (ILD-set) of $G$ if $L$ is independent and dominating with the additional property that $N (u) \cap L \neq N (v) \cap L$ for any pair of distinct $u, v \in V(G) \setminus L$. The independent location-domination number of a graph $G$ is the minimum cardinality of an ILD-set of $G$ and is denoted by $i_{\ell}(G)$. In this paper, we study the non-existence of ILD-sets of maximal outerplanar graphs and circulants graphs. In trees, we prove that \textcolor{red}{$\frac{n + 1}{3} \leq i_{\ell}(T) \leq n - 1$} for every tree $T$ of $n$ vertices. We further prove that there exists a tree $T$ with prescribed value $i_{\ell}(T)$ between these bounds. https://comb-opt.azaruniv.ac.ir/article_15137_62b8fc5cd71a689649cb3518c929fee2.pdf