Faculty Publications

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    An improved bound on weak independence number of a graph
    (2013) Bhat, R.S.; Kamath, S.S.; Surekha
    A vertex v in a graph G=(V,X) is said to be weak if d(v)≤d(u) for every u adjacent to v in G. A set S ⊆ V is said to be weak if every vertex in S is a weak vertex in G. A weak set which is independent is called a weak independent set (WIS). The weak independence number wβ0(G) is the maximum cardinality of a WIS. We proved that wβ0(G)≤ p-δ. This bound is further refined in this paper and we characterize the graphs for which the new bound is attained.
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    Review on fiber composites for sustainable high strain rate applications
    (Elsevier Inc., 2025) Lakshme Gowda, D.M.; Bhat, R.S.; Rangappa, S.M.; Siengchin, S.
    Over the past two decades, the growing demand for sustainable, high-performance materials has driven significant advancements in fiber reinforced polymer composites (FRPCs), particularly for dynamic and ballistic applications. This review provides an integrated overview of recent developments, highlighting sustainable reinforcements, novel stacking configurations, and advanced machine learning (ML) predictive approaches. Particular emphasis is placed on bio-inspired helicoidal laminates and hybrid architectures, which offer superior energy absorption, damage tolerance, and impact mitigation. Hybrid laminates incorporating satin weaves, high-modulus fibers, and compliant matrices enhance post-impact toughness and better structural integrity. Additionally, embedding a high-hardness (70–90 Shore A) rubber core with a compliant matrix mitigates conical crack propagation, improves strain rate sensitivity, and reduces delamination under both low- and high-velocity impacts. The dynamic response of FRPCs is examined using experimental techniques such as Split Hopkinson Pressure Bar (SHPB) testing and impact assessments, revealing the influence of design variables on strain-rate-dependent behavior. To support material selection and design optimization in fiber composites, ML techniques, Ashby charts, and Multi-Criteria Decision-Making (MCDM) frameworks are explored, balancing performance, sustainability, and manufacturability. Failure mechanisms such as delamination, fiber pull-out, and matrix cracking are analyzed with respect to hybridization strategies and environmental effects. Finite element analysis (FEA) tools, including ABAQUS, ANSYS AUTODYN, and LS-DYNA, are reviewed for their predictive accuracy, validated against experimental results. Standardized testing protocols (ASTM D7136, D7137, F1342; NIJ-0101.06) ensure the consistent evaluation of both flexible and rigid armor systems. The review also discusses manufacturing advancements such as resin transfer molding (RTM) and filament winding, which improve scalability and reduce waste. Non-destructive testing (NDT) methods, including acoustic emission, ultrasonic C-scanning, and X-ray CT, are highlighted for real-time damage assessment. Finally, integrating ML algorithms such as MLP, SVM, RF, and CNN with experimental and simulation data enhances predictive modeling, damage classification, and tailored composite design. This convergence of bio-inspired design, computational tools, and intelligent systems is accelerating the development of next-generation FRPCs for aerospace, defense, automotive, and civil engineering applications. © 2025 The Authors
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    On strong (weak) independent sets and vertex coverings of a graph
    (2007) Kamath, S.S.; Bhat, R.S.
    A vertex v in a graph G = (V, E) is strong (weak) if deg (v) ? deg (u)(deg (v) ? deg (u)) for every u adjacent to v in G. A set S ? V is said to be strong (weak) if every vertex in S is a strong (weak) vertex in G. A strong (weak) set which is independent is called a strong independent set [SIS] (weak independent set [WIS]). The strong (weak) independence numbers ? = s ? (G) (w ? = w ? (G)) is the maximum cardinality of an SIS (WIS). For an edge x = uv, v strongly covers the edge x if deg (v) ? deg (u) in G. Then u weakly covers x. A set S ? V is a strong vertex cover [SVC] (weak vertex cover [WVC]) if every edge in G is strongly (weakly) covered by some vertex in S. The strong (weak) vertex covering numbers ? = s ? (G)(w ? = w ? (G)) is the minimum cardinality of an SVC (WVC). In this paper, we investigate some relationships among these four new parameters. For any graph G without isolated vertices, we show that the following inequality chains hold: s ? ? ? ? s ? ? w ? and s ? ? w ? ? ? ? w ?. Analogous to Gallai's theorem, we prove s ? + w ? = p and w ? + s ? = p. Further, we show that s ? ? p - ? and w ? ? p - ? and find a necessary and sufficient condition to attain the upper bound, characterizing the graphs which attain these bounds. Several Nordhaus-Gaddum-type results and a Vizing-type result are also established. © 2006.
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    Development of nano-structured Zn-Ni multilayers and their corrosion behaviors
    (2011) Yogesha, S.; Bhat, R.S.; Venkatakrishna, K.; Pavithra, G.P.; Ullal, Y.; Hegde, A.C.
    Composition modulated multilayer alloy (CMMA) coatings of Zn-Ni was developed using single bath technique (SBT). CMMA coatings were developed galvanostatically using square current pulses. The cyclic cathode current densities (CCCDs) and number of layers were optimized for highest corrosion resistance. Experimental results showed that CMMA coating, developed at 2.0/5.0 A/dm2, having 300 layers is ?29 times higher corrosion resistant than monolithic alloy of same thickness. Tafel and impedance data revealed its good protection ability. The improved corrosion behavior exhibited by multilayers was explained using dielectric spectroscopy. The formation of multilayer and corrosion mechanism was analyzed using scanning electron microscopy (SEM). Copyright © Taylor & Francis Group, LLC.
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    Development of nano-structured cyclic multilayer Zn-Ni alloy coatings using triangular current pulses
    (2011) Bhat, R.S.; Hegde, A.C.
    Cyclic multilayer alloy (CMA) deposits of Zn-Ni were developed on mild steel from sulphate bath having thiamine hydrochloride (THC) and citric acid (CA) as additives. CMA coatings were developed galvanostatically using triangular current pulses, under different conditions of cyclic cathode current density (CCCD's) and number of layers. The corrosion behaviors of the coatings were evaluated by potentiodynamic polarization and electrochemical impedance spectroscopy methods, and were compared with that of monolayer Zn-Ni alloy of same thickness. At optimal configuration, CMA coating represented as, (Zn-Ni)2.0/5.0/300 was found to exhibit ?40 times better corrosion resistance compared to monolayer alloy, (Zn-Ni)3.0. Cyclic voltammetry study demonstrated that THC and CA have improved the appearance of the deposit by complexation with metal ions. The corrosion protection efficacy of CMA coatings was attributed to the difference in phase structure of the alloy in successive layers, evidenced by XRD analysis. The formation of multilayer and corrosion mechanism was analyzed by Scanning Electron Microscopy (SEM) study. © 2011 Allerton Press, Inc.
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    Corrosion behavior of electrodeposited Zn-Ni, Zn-Co and Zn-Ni-Co alloys
    (2011) Bhat, R.S.; Bhat, U.; Hegde, A.C.
    Zn-Ni, Zn-Co and Zn-Ni-Co alloy coatings were electrodeposited galvanostatically using sulphate bath, having THC as additive. The bath composition and operating parameters have been optimized by standard Hull cell method. The effects of current density (c.d.), pH on composition, thickness, hardness of the deposit were studied. Under all conditions of deposition, the bath followed anomalous type of codeposition with preferential deposition of less noble metal. Corrosion resistances of the coatings were measured by potentiodynamic polarization and Electrochemical Impedance Spectroscopy (EIS) method showed that under optimal conditions, the corrosion resistance of Zn-Ni-Co alloy coatings is approximately 20 times and 18 times better than Zn-Ni and Zn-Co alloys of same thickness. The Zn-Ni-Co coating under optimal c.d. (3.0 A dm-2) was found due to its inherent high dielectric barrier, evidenced impedance signals. High partial c.d. for zinc in Zn-Ni-Co alloy system supports the possibility of a synergistic catalytic effect of Co on Fe and vice versa. X-ray diffraction study clearly indicates that improved corrosion resistance of ternary alloy is due to the change in the phase structure of the coatings, compared to binary alloys. Surface morphology and composition of the coatings were examined by using Scanning Electron Microscopy (SEM), interfaced with EDX facility, respectively. The ternary Zn-Ni-Co coating may thus replace the conventional Zn-Ni and Zn-Co coatings in a variety of applications. © 2011 by CEE.
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    Corrosion stability of electrodeposited cyclic multilayer Zn-Ni alloy coatings
    (2011) Bhat, R.S.; Udupa, K.R.; Hegde, A.C.
    This paper reports on a study of electrodeposition and characterisation of cyclic multilayer coatings of Zn-Ni alloy from a sulphate bath. Cyclic multilayer alloy coatings were deposited on mild steel through the single bath technique by appropriate manipulation of cathode current densities. The thickness and composition of the individual layers of the CMA deposits were altered precisely and conveniently by cyclic modulation of the cathode current during electrodeposition. Multilayer deposits with sharp change in composition were developed using square current pulses, using thiamine hydrochloride and citric acid as additives. Laminar deposits with different configurations were produced and their corrosion behaviours were studied by AC and DC methods in 5%NaCl solution. It was observed that the corrosion resistance of the CMA coating increased progressively with the number of layers (up to certain optimal numbers) and then decreased. The decrease in corrosion resistance at high degree of layering was attributed to interlayer diffusion due to less relaxation time for redistribution of metal ions at cathode during deposition. The coating configurations have been optimised for peak performance of the coatings against corrosion. It was found that CMA coating developed at cyclic cathode current densities of 3.0/5.0 A dm-2 with 300 layers showed the lowest corrosion rate (0.112×10-2 mm/year) which is ?54 times better than that of monolithic Zn-Ni alloy, deposited from the same bath. The protection efficacy of CMA coatings is attributed to the difference in phase structure of the alloys in successive layers, deposited at different current densities, evidenced by X-ray diffraction analysis. The formation of multilayers and corrosion mechanism were examined by scanning electron microscopy. © 2011 Institute of Metal Finishing.
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    Strong (weak) edge-edge domination number of a graph
    (2012) Bhat, R.S.; Kamath, S.S.; Bhat, S.R.
    For any edge x=uv of an isolate free graph G(V,E),(N[x]) is the subgraph induced by the vertices adjacent to u and v in G. We say that an edge x, e-dominates an edge y if y ? (N[x]). A set L ? E is an Edge-Edge Dominating Set (EED-set) if every edge in E-L is e-dominated by an edge in L. The edge-edge domination number ? ee(G) is the cardinality of a minimum EED-set. We find the relation ship between the new parameter and some known graph parameters.
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    Electroplating and corrosion study of Zn-Co, Zn-Fe and Zn-Co-Fe alloys
    (2012) Bhat, R.S.; Chitaranjan Hegde, A.
    Zn-Co, Zn-Fe and Zn-Co-Fe coatings were electrodeposited on mild steel from an acid sulphate bath, using thiamine hydrochloride (THC) and citric acid (CA) as additives. Bath constituents and operating parameters were optimized by standard Hull cell method, for peak performance of the coatings against corrosion. The effect of current density (c.d.), pH on the deposit characters, such as corrosion resistance, hardness, thickness, partial current density and CCE were studied and discussed. Corrosion resistances were evaluated by Potentiodynamic polarization and electrochemical impedance spectroscopic (EIS) method. Corrosion resistance of the Zn-Co-Fe coating under optimal c.d. (3.0 A dm-2) was found due to its inherent high dielectric barrier, evidenced impedance signals. High partial current density for zinc in Zn-Co-Fe alloy coating supports the possibility of a synergistic catalytic effect of Co on Fe and vice versa. X-ray diffraction study clearly indicates that a drastic change in corrosion resistance of ternary alloy is due to the change in the phase structure of the coatings, compared to binary alloys. Surface morphology and composition of the coatings were examined by using Scanning Electron Microscopy (SEM), interfaced with Energy Dispersive X-ray Analysis (EDXA) facility, respectively. © 2012 by CEE.
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    Optimization of bright Zn-Co-Ni alloy coatings and its characterization
    (2013) Bhat, R.S.; Hegde, A.C.
    Acidic sulphate bath having ZnSO4.7H2O, CoSO4.7H2O, NiSO4.7H2O and thiamine hydrochloride (THC) and citric acid (CA) in combination, was optimized for deposition of bright Zn-Co-Ni alloy coating on mild steel. Bath constituents and operating parameters were optimized by Hull cell method, for highest performance of the coating against corrosion. The effect of current density (c.d.), on deposit characters, such as corrosion resistance and hardness, thickness were studied and discussed. Potentiodynamic polarization and electrochemical impedance spectroscopy (EIS) methods were used to assess the corrosion behaviors. The composition of deposits were determined by spectrophotometeric method and confirmed by EDX analysis. Surface morphology of the deposits was examined using scanning electron microscopy (SEM). The Zn-Co-Ni alloy, with intense peaks corresponding to Zn (100) and Zn (101) and Zn (110) phases, showed highest corrosion resistance, evidenced by X-ray diffraction (XRD) study. A new and cheap sulphate bath, for bright Zn-Co-Ni alloy coating on mild steel has been proposed, and results are discussed. © 2013 by CEE.