📄 Optimizing Sanskrit Antyakshari with Directed Graphs: A Competitive and Strategic Tool for Enhanced Play

Summary

Antyākṣarī is a chain game in which each recited verse must begin with the final syllable of the previous one, and no verse may be repeated. Shankararama Sharma (Vyoma Linguistic Labs Foundation) gives what he presents as the first formal mathematical treatment of its Sanskrit form. Verses from the Bhagavad-Gītā and Śrīman-Nārāyaṇīyam become nodes of a Directed Multigraph (DMG). Each node stores the verse's first akṣara, its final complete akṣara and its final svara, and edges link verses that may legally follow one another.

Two rule sets are compared:

• Rule Set A uses standard syllable linking.
• Rule Set B falls back to the vowel when no verse starts with the required consonant.

The analysis covers sources, sinks, cycles, isolated nodes, node degrees and longest playable chains. Longest chains are found with a DFS-with-memoization heuristic. Rule Set B nearly removes dead ends. Frequently occurring syllables, especially त, can be exploited strategically. The study is a proof of concept for an AI-assisted Antyākṣarī tool for practice and competition preparation.

Key points

• Longest chains under Rule Set A: 234 verses for the Bhagavad-Gītā and 455 for the Nārāyaṇīyam. The search is heuristic and runs in O(V² + E), so these figures are lower bounds, not proven optima.
• Speed: the combined dataset of about 1,737 verses is processed in 0.015 s. The text also gives 1,734 at one point. The graph's sparsity helps: under Rule Set A it has 96 sink nodes and 25 isolated nodes.
• Effect of Rule Set B on dead ends: sink nodes fall to 3 in the Gītā and 2 in the Nārāyaṇīyam. The combined graph has none.
• Node degrees: these are identical under both rule sets. त dominates the combined data, with 217 verse openings, 387 verse endings and a top total degree of 602. Playing high-degree nodes early is recommended as a way to make the game harder for opponents.
• Code and data: published in the GitHub repository Vyoma-Linguistic-Labs/Antyakshari-Krida. Planned extensions include metre-based rules, user-uploaded verse collections and NLP integration.