In this paper, we describe two algorithms to identify the repeating subwords in a given partial word \( w_o = w_0[1,…,n] \). The first algorithm uses the suffix tree and the second algorithm uses the valency tree. Both algorithms take linear time to identify the repeating subwords of a partial word.

We present a class of Coded Petri net languages and study some algebraic properties. The purpose of introduction of this language is to bring out its usefulness in learning theory. We introduce an algorithm for learning a finite coded Petri net language and its running time is bounded by a polynomial function of given inputs.

In this present investigation, the authors obtain Fekete-Szegő’s inequality for certain normalized analytic functions \( f(z) \) defined on the open unit disk. As a special case of this result, Fekete-Szegő’s inequality for a class of functions defined through fractional derivatives is obtained. The motivation of this paper is to give a generalization of the Fekete-Szegő inequalities obtained by Srivastava and Mishra and Ma and Minda.

This paper is mainly devoted to generate (special) (super) edge-magic labelings of graphs using matrices. Matrices are used in order to find lower bounds for the number of non-isomorphic (special) (super) edge-magic labelings of certain types of graphs. Also, new applications of graph labelings are discussed.

A well-designed interconnection network makes efficient use of scarce communication resources and is used in systems ranging from large supercomputers to small embedded systems on a chip. This paper deals with certain measures of vulnerability in interconnection networks. Let \( G \) be a non-complete connected graph and for \( S \subseteq V(G) \), let \( \omega(G – S) \) and \( m(G – S) \) denote the number of components and the order of the largest component in \( G – S \), respectively. The vertex-integrity of \( G \) is defined as

\[I(G) = \text{min}\{|S| + m(G – S) : S \subseteq V(G)\}.\]

A set \( S \) is called an \( I \)-set of \( G \) if \( I(G) = |S| + m(G – S) \). The rupture degree of \( G \) is defined by

\[r(G) = \text{max}\{\omega(G – S) – |S| – m(G – S) : S \subseteq V(G), \omega(G – S) \geq 2\}.\]

A set \( S \) is called an \( R \)-set of \( G \) if \( r(G) = \omega(G – S) – |S| – m(G – S) \). In this paper, we compute the rupture degree of complete binary trees and a class of meshes. We also study the relationship between an \( I \)-set and an \( R \)-set and find an upper bound for the rupture degree of Hamiltonian graphs.

In this paper, we establish the possibility of embedding a graph as an induced subgraph in an: elegant graph, harmonious graph, felicitous graph, cordial graph, odd-graceful graph, polychrome graph, and strongly c-harmonious graph, each with a given property, leading to prove the NP-completeness of some parameters like: chromatic number, clique number, domination number, and independence number
of these graphs.

This paper describes an approach based on modified invariant moments for recognition of multi-font English characters. The proposed method is independent of size and translation variations and shows better results under noisy conditions. The work treats isolated English characters which are normalized to a size of \( 33 \times 33 \) pixels and the image is thinned. As a pre-classification step, end points and Euler numbers have been estimated from this thinned image of the character. For size and translation invariance, the modified invariant moments suggested by Palaniappan have been evaluated. The system is trained for 7 different font styles with 364 images. A decision tree-based minimum distance nearest neighbor classifier has been adopted for classification. The system is tested for these seven fonts with various sizes of the characters between 8 to 72. A total of 7,280 character images are tested with this system and the success rate is found to be 99.65\%. The method shows encouraging results on multi-font/sized character images.

A Knowledge Based Document Management System (KBDMS) is proposed in this paper to organize, cluster, classify and discover free-text documents. Context sensitive information is discovered by means of word map, sentence map and paragraph map in an intelligent manner in this proposed system. A text learning procedure for the semantic retrieval of text documents is implemented using a hierarchy of self-organizing maps (SOM) and support vector machines (SVM). The hierarchical SOM generates histograms of paragraph maps based on the semantic similarity and these paragraph maps are trained using SVM for classification. The SVM also generates an index for each document given to it. The proposed system is scalable and capable of discovery of documents from a huge amount of free-text documents. It is tested over a maximum of 100,000 text documents with 75-80\% accuracy in the context-sensitive discovery of free-text documents.

The purpose of this paper is to construct the membership functions of performance measures in bulk arrival queuing systems with arrival rate and service rate being fuzzy numbers. Thus, this paper develops the parametric programming approach to derive the membership functions of the steady-state performance measures in bulk arrival queuing systems with varying batch size. On the basis of a cut representation and extension principle, a parametric programming is formulated to describe the family of crisp bulk arrival queues. The performance measures are expressed by membership functions rather than crisp values, which completely conserve the fuzziness of input information when some data of bulk arrival queuing systems are ambiguous.

In order to establish the mathematical basis for connections between molecular structures and physicochemical properties of chemical compounds, some topological indices have been put forward. Among them, the Wiener index is one of the most important topological indices. The sum of distances of all pairs of vertices in a connected graph is known as Wiener index or Wiener number. All structural formulas of chemical compounds are molecular graphs where vertices represent the set of atoms and edges represent chemical bonds. A graph is said to be detour saturated if the addition of any edge results in an increased greatest path length. The characteristic graph of a given benzenoid graph consists of vertices corresponding to hexagonal rings of the graph; two vertices are adjacent if and only if the corresponding rings share an edge. A benzenoid graph is called Cata-condensed if its characteristic graph is a tree. In this paper, we derive Wiener indices for characteristic graphs of benzenoid graphs in the form of hexagonal rings, which are detour-saturated trees.