SECURE METRIC DIMENSION OF ALTERNATE SNAKE GRAPHS

We study the NP-hard problem of determining the secure metric dimension of graphs. A resolving set uniquely identifies each vertex by its distance vector to the set; the smallest is the metric basis, and its size is the metric dimension. A set is secure if each outside vertex can replace an inside one while preserving resolvability. Computing this parameter is NP-complete and has applications in routing, image processing, and network verification. This paper determines the secure metric dimension for alternate snake graphs, including k-polygonal, double, and triple alternate triangular snakes.