Strategic Security Zoning Via Chromatic Graph Theory: An Optimized Patrol Allocation for Nigeria’s Geopolitical Regions

Geographically distributed security risks throughout Nigeria tend to spread from one state to another via shared borders and movement routes, ensuring the requirement for an optimized and conflict-free security deployment strategy. In this work, a framework for allocating and deploying available security resources in a manner that avoids inter-unit conflicts in a Nigerian setting is proposed by formulating a graph-coloring model that represents the six geopolitical zones in a two-dimensional coordinate plane as map graphs and allocates states as vertices and borders between them as edges. For each zone, a backtracking algorithm based on an adjacency matrix approach is applied with a view to determining the chromatic numbers χ(G) that represent the optimal minimum needed non-conflicting security patrol units and schedules needed to avoid interference and overlap on interstate levels for enhanced operational efficiency and effectiveness. From the results, it can be observed that while the Northeast geopolitical zone has the highest connectivity and insurgent activities, security deployment needs χ(G) = 4 units, whereas for the North-Central, Northwest, Southeast, South-South, and Southwest zones, security deployment needs χ(G) = 3 units. This indicates the immediate applicability of security resource allocation into partitioned time schedules for nationwide security patrol network deployment and regional security force coordination. By appropriating map graphs on a plane into a real-time applicability tool, the research highlights the applicability of computational graph theory concepts for optimizing security resource planning from conventional-based approaches toward efficient strategies involving minimum resource spending with the highest operational ranges to achieve the UN Sustainable Development Goal.