Graph Theory & Formal Methods
Spectral structure, graph energy, eccentricity, extremal questions, graph algorithms, complexity and machine-checkable certificates.
Assistant Professor · Program Head, Data Science Programs · Ph.D. Mathematics · Open Research
Mathematics → Networks → Reliable Scientific AI
I build research from graph theory and formal graph methods through networked systems, molecular and biomolecular graphs, and reliable scientific AI—using rigorous mathematics and reproducible computation to make scientific evidence more interpretable, auditable and trustworthy.
Dr. Sunilgar L. GusaiGraph Theory · Reliable Scientific AI
λ Spectral Methods
G Graph Intelligence
✓ Reproducible Science
Academic Identity
One research programme, from mathematical structure to reliable prediction.
My work is driven by a simple principle: structural mathematics is most valuable when its claims remain testable against real systems, and computational models are most useful when their limitations are visible.
I am an Assistant Professor of Mathematics and Program Head for Data Science Programs at Marwadi University, Rajkot, working across mathematics, computing and data-oriented programmes. My doctoral and continuing research centres on spectral graph theory, graph energy, eccentricity-driven invariants and mathematically interpretable graph descriptors.
A central strand of this work is Vertex Eccentricity Labeled Energy (VELE). I study its structural theory and also test where eccentricity-sensitive spectral information is useful—or insufficient—in applied network settings.
My current programme extends this foundation into network resilience, molecular graph representations, QSPR/QSAR, uncertainty-aware scientific machine learning, and methods for learning when explicit scientific rules should or should not be trusted.
Research Architecture
Four connected directions, eight open programmes.
The programme now spans pure and computational graph theory, resilient networked systems, molecular and biomolecular graph modelling, and reliability-focused scientific AI.
Networked Systems & Resilience
Power grids, road networks, failure-sensitive screening, flood hazards, transfer evaluation and budgeted intervention.
Molecular & Biomolecular Graphs
QSAR, representation degeneracy, scientific rules, residue-contact networks, mutation geometry and protein stability.
Reliable Scientific AI & Evidence
Distribution shift, calibration, conformal prediction, abstention, evidence consistency, provenance and reproducible decision analysis.
Spectral graph invariantsVELEGraph algorithmsEvidence certificatesNetwork resiliencePower-grid screeningFlood-road networksProtein residue networksQSPR / QSARRepresentation limitsConformal predictionGeographic shiftScientific rulesReproducibility
Open Research & Reproducibility
An eight-programme open research ecosystem.
Public repositories are treated as scientific artefacts: code, frozen outputs, provenance, validation, claim boundaries and negative findings remain inspectable.
Current frontierNewest public programmes
Mutation Geodesic Shielding for Protein Stability
A mutation-centered graph-geodesic framework asking when local residue-network geometry is exposed to a substitution and when alternative bypass routes preserve shortest-path structure.
382,543 substitutions38.5% whole-mutation shielding3 evidence layers
- Target-free certificate characterization
- Independent stability association retained with limits
- Explicit-mutant structural comparison and CI validation
Assam Road Inspection Benchmark
A leakage-controlled, multi-event benchmark for prioritising flood-exposed road inspection under unseen events, held-out geography, sparse hazard observations and limited budgets.
4 flood events211,175 edge-event observations135 spatial blocks
- Leave-one-event-out and grouped spatial validation
- Two inspection-cost models and six budget levels
- Negative and shortcut findings preserved explicitly
Claim–Evidence Consistency in Labeled Graphs
A theory-first framework for globally coherent claim-to-evidence alignment, automata-defined support, verification certificates, tractable graph classes and local correction.
12/12 tests5,000 claim vertices180 evidence-cover instances
- Polynomial verification vs NP-complete global consistency
- Exact algorithms on trees and bounded treewidth
- Machine-checkable certificates and frozen validation
Global MSW Reliability Under Geographic Shift
A reliability-first audit of municipal waste-service prediction under unseen regions, subgroup shift, uncertainty and service-deficit prioritisation.
4 reliability lensesLORO geographic transferv1.0.0 frozen release
- Geographic transfer separated from in-distribution accuracy
- Subgroup bias and conformal uncertainty auditing
- Decision consequences evaluated from frozen predictions
Established open researchCore reproducibility programmes
VELE Power-Grid Vulnerability Screening
An eccentricity-sensitive structural screening framework evaluated against island-aware DC-flow behaviour and service consequences across IEEE/MATPOWER systems.
6 systems784 branch outages1,692 progressive states
- Executable MATPOWER 8.1 / GNU Octave cross-check
- Explicit topology-only failure modes retained
- Frozen reproducibility release and machine-readable outputs
EGFR Graph QSAR — Representation Limits
A controlled comparison asking what EGFR pIC50 signal survives compression to 19 classical graph invariants—and where that representation becomes non-identifying.
10,056 compounds19 graph invariants41.6% in collision groups
- Graph19 vs RDKit2D vs ECFP4 under matched validation
- Mechanism-resolved descriptor degeneracy analysis
- Scaffold shift, uncertainty and chemical-space diagnostics
Applicability-Gated Molecular AI
Rule-residual learning that keeps an explicit scientific rule visible as a fallible expert and learns when the rule should be trusted, corrected or audited under chemical-space shift.
5 molecular resources3 split families5 seeds
- Explicit rule reliance and independent rule-failure diagnosis
- Negative controls and mixed findings kept visible
- External B3DB transfer with discrimination/calibration analysis
Calibration Transfer of Conformal Prediction
Uncertainty-aware concrete-strength modelling across physically interpretable supplementary-cementitious-material composition regimes.
1,030 observations427 mix designs30 repetitions / cell
- Grouped design limits cross-age mixture leakage
- Graded shifts and complete composition holdouts
- Machine-readable verification to numerical precision
01ReproducibleExecutable workflows & pinned environments
02ValidatedIndependent checks & sensitivity analysis
03TraceableProvenance & machine-readable evidence
04RestrainedNegative findings and limits stay visible
Published & Accepted Scholarship
Research that has crossed an editorial milestone.
Published records are linked where a stable DOI or publication page is available. Accepted work is labelled separately until a public publication record is verifiable.
2026
Edge Failure Sensitivity of Wiener and Harary Indices in Classical Network Graphs
Sunilgar Gusai. International Journal of Scientific Development and Research, 11(9), b394–b402, September 2026.
Accepted
Explainable Machine Learning for Real-Time Cyber Threat Detection: An Intelligent Framework for Adaptive Information Security
Computer and Decision Making (COMDEM) · Manuscript CDM_121 · accepted for publication on 30 September 2026; public publication metadata pending.
2026
Eccentricity-Based Bounds for the Spectral Radius of Graph Matrices
Sunilgar L. Gusai. International Journal of Science and Research, Vol. 15, pp. 681–686, 2026.
2025
On Vertex Eccentricity Labeled Energy of a Graph
Sunilgar Gusai, Vinodray Kaneria, Manoharsinh Jadeja. International Journal of Basic and Applied Sciences, 14(4), 339–350, 2025.
Funded Research
The Study on Variants of Graph Energy
Seed Grant · Marwadi University
₹80,000Principal Investigator
Supporting investigations in spectral graph theory, graph-energy measures, VELE, structural analysis and computational network applications.
Teaching & Mentoring
Mathematical foundations for modern computing.
I teach undergraduate and postgraduate students across mathematics, computing and data-oriented programmes.
My teaching emphasizes conceptual clarity, analytical reasoning, and the connection between mathematical foundations and real computational problems.
Linear AlgebraCalculusDiscrete MathematicsOperations ResearchProbabilityStatisticsApplied MathematicsOptimization
Application contexts include data analysis, machine-learning foundations, network analysis, algorithmic thinking and mathematical modelling.
Academic Leadership & Service
Research, teaching and institutional contribution.
Program Head · Data Science
Academic planning, curriculum coordination, faculty coordination, student mentoring and programme-quality support for Data Science programmes.
Area Chair · Advanced Computing
Coordinating advanced-computing research themes across graph/game theory, optimization, parallel and green computing, quantum computing and related areas.
Assistant Professor · Mathematics
Teaching, mentoring and interdisciplinary research across mathematics, computer applications, AI and data-oriented programmes.
Academic Coordination
Timetable operations, examinations, documentation, industrial exposure, student activities, committees and institutional quality processes.
Latest
Recent research milestones
Open-research ecosystem expanded to eight public programmes
New public artefacts now include mutation geodesic shielding for protein stability, an Assam flood-road inspection benchmark, claim–evidence consistency in labeled graphs, and global MSW reliability under geographic shift.
Cyber-threat manuscript accepted for publication
“Explainable Machine Learning for Real-Time Cyber Threat Detection” was accepted by Computer and Decision Making (COMDEM), manuscript CDM_121.
Wiener–Harary edge-failure paper published
The exact sensitivity study for classical network graph families appeared in IJSDR, Volume 11 Issue 9, pages b394–b402, with DOI 10.56975/ijsdr.v11i9.311920.
EGFR Graph QSAR reproducibility programme strengthened
Mechanism-resolved representation degeneracy, precision sensitivity, second-learner checks and ECFP4 collision analysis were added to the public research record.
Ph.D. in Mathematics
Completed doctoral research in graph theory, graph energy and related mathematical applications at Saurashtra University.
Research & Academic Contact
Interested in rigorous graph-theoretic or computational collaboration?
Open to serious collaboration in graph theory and algorithms, network resilience, molecular and biomolecular graph modelling, reliable scientific AI, evidence verification and reproducible computational research.