Clique Irreducibility of Some Iterative Classes of Graphs

In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if and only if every triangle in G has a vertex of degree two. The conditions for the iterations of line graph, the Gallai graphs, the anti-Gallai graphs and its iterations to be clique irreducible and clique vertex irreducible are also obtained.

Clique Irreducibility and Clique Vertex Irreducibility of Graphs

A graphs G is clique irreducible if every clique in G of size at least two,has an edge which does not lie in any other clique of G and is clique reducible if it is not clique irreducible. A graph G is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G and clique vertex reducible if it is not clique vertex irreducible. The clique vertex irreducibility and clique irreducibility of graphs which are non-complete extended p-sums (NEPS) of two graphs are studied. We prove that if G(c) has at least two non-trivial components then G is clique vertex reducible and if it has at least three non-trivial components then G is clique reducible. The cographs and the distance hereditary graphs which are clique vertex irreducible and clique irreducible are also recursively characterized.

Ecotoxic Metal Records and its Degree of Geochemical Symphony in the Niche of Cochin Estuarine System- A Theraptic Perspective

The heavy metal contamination in the environment may lead to circumstances like bioaccumulation and inturn biomagnification. Hence cheaper and effective technologies are needed to protect the precious natural resources and biological lives. A suitable technique is the one which meets the technical and environmental criteria for dealing with a particular remediation problem and should be site-specific due to spatial and climatic variations and it may not economically feasible everywhere. The search for newer technologies for the environmental therapy, involving the removal of toxic metals from wastewaters has directed attention to adsorption, based on metal binding capacities of various adsorbent materials. Therefore, the present study aim to identify and evaluate the most current mathematical formulations describing sorption processes. Although vast amount of research has been carried out in the area of metal removal by adsorption process using activated carbon few specific research data are available in different scientific institutions. The present work highlights the seasonal and spatial variations in the distribution of some selected heavy metals among various geochemical phases of Cochin Estuarine system and also looked into an environmental theraptic/remedial approach by adsorption technique using activated charcoal and chitosan, to reduce and thereby controlling metallic pollution. The thesis has been addressed in seven chapters with further subdivisions. The first chapter is introductory, stating the necessity of reducing or preventing water pollution due to the hazardous impact on environment and health of living organisms and drawing it from a careful review of literature relevant to the present study. It provides a constricted description about the study area, geology, and general hydrology and also bears the major objectives and scope of the present study.

Mathematical Morphology on Hypergraphs Using Vertex-Hyperedge Correspondence

The focus of this paper is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of dual adjunctions between the vertex set and the hyperedge set of a hypergraph , by defining a vertex-hyperedge correspondence. This allows us to recover the classical notion of a dilation/erosion of a subset of vertices and to extend it to subhypergraphs of . This paper also studies the concept of morphological adjunction on hypergraphs for which both the input and the output are hypergraphs