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While the problem of generating random graphs has received much attention, the problem of generating graphs for specific classes has not been studied much. In this dissertation, we propose schemes for generating chordal graphs, weakly chordal graphs, and strongly chordal graphs. We also present semi-dynamic algorithms for chordal graphs and strongly chordal graphs. As an application of a completion technique for chordal graphs, we also discuss a 1-round algorithm for approximate point placement in the plane in an adversarial model where the distance query graph presented to the adversary is chordal.The proposed generation algorithms take the number of vertices, n, and the number of edges, m, as input and produces a graph in a given class as output. The generation method either starts with a tree or a complete graph. We then insert additional edges in the tree or delete edges from the complete graph. Our algorithm ensures that the graph properties are preserved after each edge is inserted or deleted. We have also proposed algorithms to generate weakly chordal graphs and strongly chordal graphs from an arbitrary graph as input. In this case, we ensure the graph properties will be achieved on the termination of the conversion process.We have also proposed a semi-dynamic algorithm for edge-deletion in a chordal graph. To the best of our knowledge, no study has been done for the problem of dynamic algorithms for strongly chordal graphs. To address this gap, we have also proposed a semi-dynamic algorithm for edge-deletions and a semi-dynamic algorithm for edge-insertions in strongly chordal graphs.

Crude press muds a sugar industry waste were collected from four sugar mills of Bangladesh. Crude press mud as well as its water soluble and water insoluble portion and extracted wax were studied for its proximate analysis, physico-chemical properties, elemental and wax composition. The proximate analysis of crude press mud showed the presence of moisture (67.95–76.53), nitrogen (1.63–2.29), ash (19.28–30.76), sugar (12.10–13.29) and crude wax (6.70–11.01). Acid value (26.95–27.68), saponification value (102.59–103.01) and iodine value (6.72–6.82) were also studied of the extracted wax. The GLC analysis showed linolenic (45.54%), oleic (27.28%) and palmitic acid (23.59%) were the predominant acids in the crude wax. The XRF spectrometric analysis of the elemental composition showed the presence of Ca (21.30–29.97%), Si (9.53–9.94%), P (8.40–9.52%), S (3.77–7.36%) and K (2.51–4.08%) in crude press mud, Ca (19.83–31.93%), K (8.76–13.52%), S (7.93–16.02%) and Mg (4.14–7.75%) in water soluble portion press mud and Ca (21.77–30.68%), K (1.62–3.41%), S (3.49–7.09%), P (9.0–11.31%), Al (2.40–2.93) and Si (10.50–10.54%) in water in-soluble portion press mud. The Fourier transform infrared analysis, Thermo gravimetric, Derivative thermo gravimetric and differential thermal analysis of press mud were also carried out. These analyses may find the suitability to enrich the micronutrients in restoring the soil composition and also find possibility to use in agriculture, horticulture and aquaculture based industries. Moreover, press mud wax may have an alternative use of carnauba wax.

The essential oil of Zingiber officinale Rosc. was extracted from China and Bangladeshi varieties and yielded 0.21% and 0.23 % by hydro-distillation method on fresh weight basis respectively. Fifteen compounds were identified and quantified by GC-MS. The major constituents of China and Bangladeshi ginger essential oils were zingiberene 38.10 % and 41.49%, β-phellandrene 12.0% and 9.92%, α-citral 11.48% and 9.76 %, α-curcumene 9.22% and 11.58%, camphene 5.94% and 4.60% , β-bisabolene 4.39% and 5.0% respectively. The IC50 (DPPH method ) values were found 61.18 µg/mL and 56.71 µg/mL with the highest inhibition of 78.49 % and 80.77% and the LC50 values in the brine shrimp lethality cytotoxicity bioassay were found 0.4842 µg/mL and 0.7151 µg/mL in China and Bangladeshi ginger essential oil respectively. Both the essential oils showed significant activities against some gram positive, gram negative bacteria and fungi. The proximate composition of the China and Bangladeshi variety showed the ash (7.12±0.151, 8.15±0.18%), protein (5.47±0.19, 6.60±0.16%), crude fibre (4.32±0.10, 4.61±0.12%), carbohydrate (16..06±0.35, 18.38±0.41) and food energy (70.50±0.89, 81.74±1.01 kcal/100g.) respectively. The elemental compositions of the both varieties were found rich in Ca, Mg, Fe, Al, Se, Na and K. These results indicate the quality composition of the two varieties may find interest in spice and culinary industries as well as in medicinal preparation.

Circuit realizations obtained from existing logic synthesis approaches may not be optimal and thus one commonly applies post-synthesis optimization techniques to get better realization of the circuits. This thesis proposes two new templates (templates 4 and 7) for positive and negative control Toffoli gates as well as proposing algorithms for post synthesis optimization of reversible positive and negative control Toffoli networks by utilizing the set of templates. When applying the templates to circuits generated by the improved shared cube synthesis approach [23] a reduction in quantum cost was achieved for 86 of the 110 circuits. On average a 21:34% reduction in quantum cost was achieved, and in some cases up to 53:58% reduction was obtained. [23] N. M. Nayeem and J. E. Rice. Improved ESOP-based synthesis of reversible logic. In Proceedings of the 2011 Reed-Muller Workshop , pages 57–62, 2011.

There is an extensive literature on dynamic algorithms for a large number of graph theoretic problems, particularly for all varieties of shortest path problems. Germane to this paper are a number fully dynamic algorithms that are known for chordal graphs. However, to the best of our knowledge no study has been done for the problem of dynamic algorithms for strongly chordal graphs. To address this gap, in this paper, we propose a semi-dynamic algorithm for edge-deletions and a semi-dynamic algorithm for edge-insertions in a strongly chordal graph, \\(G = (V, E)\\), on \\(n\\) vertices and \\(m\\) edges. The query complexity of an edge-deletion is \\(O(d_u^2d_v^2 (n + m))\\), where \\(d_u\\) and \\(d_v\\) are the degrees of the vertices \\(u\\) and \\(v\\) of the candidate edge \\(\\{u, v\\}\\), while the query-complexity of an edge-insertion is \\(O(n^2)\\).

Strongly chordal graphs are a subclass of chordal graphs. Farber also established a number of different characterisations for this class of graphs. These include an intersection graph characterisation that is analogous to a similar characterisation for chordal graphs. Seker et al. exploited this characterisation of chordal graphs to obtain an algorithm for generating them. In this paper, we propose an algorithm to show that strongly chordal graphs can also be generated using their intersection graph characterisation.

Microbial inoculants that integrate plant growth promotion, pathogen suppression, and pollutant degradation are central to sustainable agriculture. Here, we report the genomic and phenotypic characterization of Lysinibacillus capsici BCSIR-Raj-01, an endophyte isolated from citrus leaves in Bangladesh. The 4.62 Mb genome encodes 4,699 coding sequences and displays an open pangenome with loci linked to stress adaptation, xenobiotic degradation, and secondary metabolite biosynthesis. Genome mining revealed complete pathways for indole-3-acetic acid (IAA) production, siderophore biosynthesis, and phosphate metabolism, alongside gene clusters for bacteriocins, lantibiotics, terpenes, and polyketides. Nitrogen cycling genes indicated diazotrophic growth potential and a truncated denitrification pathway. Phenotypic assays validated these predictions: L. capsici BCSIR-Raj-01 solubilized phosphate, produced IAA and siderophores, grew on hydrocarbons, and exhibited diazotrophic activity. Notably, the strain showed potent larvicidal activity against Culex and Anopheles larvae, suggesting ecological roles beyond plant association. Together, these results establish L. capsici BCSIR-Raj-01 as a multifunctional bacterium with potential applications in crop improvement, bioremediation, and biological vector control. The challenges of modern agriculture and environmental sustainability demand microbial solutions that deliver multiple functions. Lysinibacillus species are increasingly recognized for such versatility, but their genomic basis remains poorly resolved. Our study provides the first genome-enabled framework for understanding multifunctionality in L. capsici. By combining whole-genome sequencing with phenotypic validation, we show that BCSIR-Raj-01 harbors biosynthetic clusters, stress adaptation loci, and xenobiotic degradation genes while also expressing experimentally confirmed traits, including phosphate solubilization, IAA and siderophore production, nitrogen fixation, hydrocarbon utilization, and larvicidal activity. This integration of plant growth promotion, biocontrol potential, and pollutant degradation positions L. capsici BCSIR-Raj-01 as a next-generation bioinoculant. Beyond broadening the functional scope of Lysinibacillus, our findings highlight how genome-guided approaches can identify microbes with cross-sectoral applications in agriculture, bioremediation, and vector management.

We propose a scheme for generating a weakly chordal graph from a randomly generated input graph, G = (V, E). We reduce G to a chordal graph H by adding fill-edges, using the minimum vertex degree heuristic. Since H is necessarily a weakly chordal graph, we use an algorithm for deleting edges from a weakly chordal graph that preserves the weak chordality property of H. The edges that are candidates for deletion are the fill-edges that were inserted into G. In order to delete a maximal number of fill-edges, we maintain these in a queue. A fill-edge is removed from the front of the queue, which we then try to delete from H. If this violates the weak chordality property of H, we reinsert this edge at the back of the queue. This loop continues till no more fill-edges can be removed from H. Operationally, we implement this by defining a deletion round as one in which the edge at the back of the queue is at the front.We stop when the size of the queue does not change over two successive deletion rounds and output H.

We propose a scheme for generating a weakly chordal graph on n vertices with m edges. In this method, we first construct a tree and then generate an orthogonal layout (which is a weakly chordal graph on the n vertices) based on this tree. In the next and final step, we insert additional edges to give us a weakly chordal graph on m edges. Our algorithm ensures that the graph remains weakly chordal after each edge is inserted. The time complexity of an insertion query is O(n^3) time and an insertion takes constant time. On the other hand, a generation algorithm based on finding a 2-pair takes O(nm) time using the algorithm of Arikati and Rangan [1].

Strongly chordal graphs are a subclass of chordal graphs. The interest in this subclass stems from the fact that many problems which are NP-complete for chordal graphs are solvable in polynomial time for this subclass. However, we are not aware of any algorithm that can generate instances of this class, often necessary for testing purposes. In this paper, we address this issue. Our algorithm first generates chordal graphs, using an available algorithm and then adds enough edges to make it strongly chordal, unless it is already so. The edge additions are based on a totally balanced matrix characterizations of strongly chordal graphs.