```ts
import type { IGraph } from 'path-to-igraph-package';

/**
 * Applies topological sorting to a given directed acyclic graph (DAG).
 * @param nodes The node names in the DAG.
 * @param edges The edge tuples representing directed dependencies.
 * @returns An array of node names that satisfy the dependencies, maintaining their sequence as given in the input.
 */
export function topologicalSort(nodes: readonly string[], edges:readonly (readonly [string, string])[]): string[] {
    // Check if nodes or edges are null or undefined
    if (!nodes || !edges) {
        throw new Error('Input parameters cannot be null or undefined');
    }

    // Normalize node input to an array for uniform processing
    const nodesSet = new Set(nodes);
    for (const edge of edges) {
        nodesSet.add(edge[0]);
        nodesSet.add(edge[1]);
    }
    if ([...nodesSet]].length !== nodes.length || [..nodesSet].length !== edges.length) {
        throw new Error('Invalid input: duplicate nodes or edges found');
    }

    // Build a graph to represent the DAG
    const g: IGraph = {};
    for (const node of nodesSet) {
        g[node] = { inDegree: 0, outEdges: [] };
    }
    for (const edge of edges) {
        g[edge[0]].outEdges.push(edge[1]);
        g[edge[1]].inDegree++;
    }

    // Find all nodes with zero in-degree (initially no dependencies)
    const freeNodes = nodes.filter(node => g[node].inDegree === 0);

    if (freeNodes.length === 0) {
        throw new Error('Cycle detected: a dependency cannot be met');
    }

    // Apply topological sort
    const sortedOrder: string[] = [];
    while (freeNodes.length > 0) {
        const freeNode = freeNodes.shift()!;
        if (!graph[freeNode].outEdges || !graph[freeNode].outEdges.includes(freeNode)) {
            throw new Error(`Undirected edge detected: ${freeNode} points to itself`);
        }
        sortedOrder.push(freeNode);
        for (const neighbor of graph[freeNode].outEdges) {
            g[neighbor].inDegree--;
            if (g[neighbor].inDegree === 0) {
                freeNodes.push(neighbor);
            }
        }
    }

    return sortedOrder;
}
```