A Low-Cost Socio-Culturally Situated Mental Health Intervention for the Well-Being of Pakistani Young Women: A Reflective Narrative

The paper sets out to briefly discuss mental health challenges faced by Pakistani young women, and brings out an innovative solution through a multidisciplinary approach, i.e, socio-culturally situated low-cost digital intervention. The paper begins with an overview of mental health issues. It then sheds light on the scope of open education and innovation in Pakistan. Finally, through a reflective narrative approach, I have explored my personal journey of becoming a networked practitioner, and how an open educational website emerged to intersect the needs of Pakistani young women. Data is gathered from 137 reflective diary entries and analyzed through narrative analysis approach. Digital literacy and open networking practices have shaped my digital identity and allowed me to embrace open scholarship. Networking and collaboration have helped me filtering Open Educational Resources (OERs). Further, collaborative activities encouraged participants to become the co-producers of resource development. Overall, an adaptation of low-cost technology has potentially helped participants to reflect and embrace their personal identities.

Multilevel and Antipodal Labelings for Families of Graphs

A radio k-labeling c of a graph G is a mapping c : V (G) → Z+ ∪ {0}, such that d(x, y) + |c(x) − c(y)| ≥ k + 1 holds for every two distinct vertices x and y of G, where d(x, y) is the distance between any two vertices x and y of G. The span of a radio k-labeling c is denoted by sp(c) and defined as max{|c(x) − c(y)| : x, y ∈ V (G)}. The radio labeling is a radio klabeling when k = diam(G). In other words, a radio labeling is a one-to-one function c : V (G) → Z+ ∪ {0}, such that |c(x) − c(y)| ≥ diam(G) + 1 − d(x, y) for any pair of vertices x, y in G. The radio number of G denoted by rn(G), is the lowest span taken over all radio labelings of the graph. When k = diam(G) − 1, a radio klabeling is called a radio antipodal labeling. An antipodal labeling for a graph G is a function c : V (G) → {0, 1, 2, ...}, so that d(x, y) + |c(x) − c(y)| ≥ diam(G) for all x, y ∈ G. The radio antipodal number for G denoted by an(G), is the minimum span of an antipodal labeling admitted by G. In this thesis, we investigate the exact value of the radio number and radio antipodal number for different family of graphs. Further more, we also determine the lower bound of the radio number for some cases.