The Restricted Rung Wiener Index of Layered Graphs

Authors

  • Sara Shokrollahi Yancheshmeh Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

Abstract

In transportation and communication networks, inter-layer routing through fixed gateways inflates path costs compared to unrestricted shortest paths.

To quantify this overhead, we introduce the Restricted Rung Wiener (RRW) index, a distance-based measure for layered graphs with mandatory crossover constraints. We derive closed-form expressions for ladder, grid, and circular prism graphs.

Linear topologies exhibit quadratic overhead in displacement from central gateways. Grids incur an unavoidable $\Theta(N^3)$ penalty independent of layer count, even under optimal placement. Circular prisms, due to rotational symmetry, yield uniform overhead across all gateway choices.

These results provide quantitative guidelines for gateway optimization in constrained multi-layer networks.

Published

2026-06-16

Issue

Vol. 20

Section

Vol. 20, No. 3, (2026)

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