The Role Of Attachment Style And Marital Quality In Attachment Injury Couples

The attachment system is thought to facilitate relationship goals by motivation seeking and bonding activities with significant others, particularly under times of stress (Bowlby, 1982). Attachment theory has also contributed to further understanding the marital relationship in terms of profound psychological and physiological interdependence. It is perhaps this interdependence that causes damage to the quality of attachment relationship. Hence, attachment injury is defined as “a specific incident or event in which one partner is unresponsive and inaccessible when one partner cries out for help in extreme need” (Johnson & Makinen, 2001). Therefore, marital distress or breakup in couple’s relationships does not happen suddenly, so understanding of attachment injury in relation to individual’s marital quality and attachment style would help practitioners to be equipped for appropriate and effective inventions. Further it would also help counsellors and mental health professionals to be familiar with the complexities of the topic by dealing with consequences of an attachment injury ethically and competently.  Therefore our study aimed at examining the prevalence and nature of attachment injury and its effect on marital quality, in a group of married heterosexual couples. It also attempted to associate attachment styles with and without attachment injury in couples. The study employed cross-sectional exploratory design with a set of self-administered measures. The sample comprised of 400 married individuals from urban Bangalore. Statistical results showed those individuals who were experiencing attachment injury are associated with poor marital quality. It was also seen that attachment injury was found to be associated with gender and insecure attachment style. Therefore our findings suggest that poor marital quality with insecure attachment style plays an important role in attachment injury over time. Based on the attachment style, further intervention strategies and effective programs should be designed for marital counselling. And marital enrichment programs may be useful to enhance marital quality to prevent the marital distress or breakups.

Mathematical Aspects of Some Graph Invariants

A graph invariant is a numerical quantity that remains unchanged under graph isomorphism. Topological indices are graph invariants that represent certain topological features of a graph. For example, connectivity, planarity, girth and diameter are topological features of a graph. Similarly, degrees and distances in a graph are examples of some basic topological features. Some topological indices of a graph can be determined solely in terms of vertex degrees or in terms of distances between the vertices. The former is called a degree-based index and the later is a distance-based index. Another type of topological invariants is the spectrum-based indices that are obtained from the eigenvalues of a graph. Finding an extremal graph with respect to a topological index is the problem of determining a graph maximizing or minimizing the value of that parameter among all graphs of fixed order. Topological descriptors are used in QSAR/QSPR studies to correlate physico-chemical properties of molecules. Our primary focus in this thesis is the study of extremal graphs with respect to some distance-based topological invariants. The graphs on which we emphasize in this part include connected n-vertex graphs with n−1 edges (i.e. trees), connected n-vertex graphs containing n edges (i.e. unicyclic graphs) and connected n-vertex graphs with n + 1 edges (i.e. bicyclic graphs), where bicyclic graphs may contain two or three cycles. We also study the corresponding extremal conjugated graphs with respect to these indices. We further our investigation to compute closed analytical formulas for some recently defined distance-based indices of join and corona product of any finite number of graphs. Moreover, we compute distance-based indices of some 3-fence graphs and their line graphs. We also compute these indices of the finite square grid and its line graph. The mathematical concept of estimation can be defined as a process of approximating a desired result with a statistical technique or software tool. The second aim of this thesis is to estimate two spectrum-based indices for the molecular graphs of some nanotubes. More results of such kind are obtained for all nanocones with one arbitrary cycle as the core.