Anisha Jean Mathias - Personal Website

About Me

I am a Postdoctoral Research Associate in the Department of Mathematics at the University of Arizona. Think of me as a "network explorer". I’m passionate about analyzing networks, from abstract graphs to real-world ecosystems. During my Ph.D., my primary research focused on determining the minimum number of nodes needed to cover a signed graph, a concept known as "domination in signed graphs." Now, I’m excited to apply this fascination with networks to the study of dolphin movements. Using tools like R and statistical modeling, I’m working to uncover hidden patterns within these networks, where each data point contributes to a bigger, fascinating story. To learn more about my work, dive deeper into this site and to connect to me, you can reach out at anishajmathias@arizona.edu.

Publications

A. J. Mathias, V. Sangeetha, and M. Acharya, "A study on the restrained domination number in diverse families of derived signed graphs," Discrete Mathematics, Algorithms and Applications, 2025.
A. J. Mathias, V. Sangeetha, and M. Acharya, "Restrained critical and abundant signed graphs," Advances & Applications in Discrete Mathematics, vol. 38, no. 1, 2023.
A. J. Mathias, V. Sangeetha, and M. Acharya, "Critical concepts of restrained domination in signed graphs," Discrete Mathematics, Algorithms and Applications, vol. 14, no. 6, pp. 1-11, 2022.
A. J. Mathias, V. Sangeetha, and M. Acharya, "Restrained domination in signed graphs," Acta Universitatis Sapientiae, Mathematica, vol. 12, no. 1, pp. 155-163, 2020.
A. J. Mathias, "Edge Domination on Graph Variations," International Journal of Mathematics And its Applications, vol. 6, no. 1, pp. 185-193, 2018.

Teaching

2025: University of Arizona, USA
- MATH/DATA 363: Introduction to Statistical Methods
2023: St Aloysius College, India
- MATH G 503 DC1.1: Numerical Analysis
- MATH G 503 OE1.1(B): Applied Mathematics
2022: St Aloysius College, India
- MATH G 503 DC1.1: Elementary Graph Theory
- MATH G503 OE1.1(A): Introductory Mathematics
2020: CHRIST(Deemed to be University), India
- MAT551B: Mathematical Modelling using Python
- MAT451: Introduction to Mathematical Modelling using Python
- BBA134: Business Mathematics
2019: CHRIST(Deemed to be University), India
- MAT 651C: Computational and Applied Mathematics using Python
- MAT 651: Complex Analysis using Python
- MAT 351: Introduction to Python Programming

Thesis

A study on domination in signed graphs :
Signed graphs, which represent the positive and negative interactions between networks, have gained signifcant attention in various felds, particularly social network analysis. Domination, a fundamental concept in graph theory, is important in understanding the structural characteristics of graphs and determining the minimum number of vertices needed to cover the entire graph. However, research on domination in the context of signed graphs has been limited, with most studies focusing on graphs.

This thesis explores a variant of domination called restrained domination in signed graphs and investigates the characteristic properties of these signed graphs in relation to the restrained domination number. Throughout the thesis, we establish exact values and bounds for the restrained domination number in diferent classes of signed graphs. Additionally, we examine the restrained domination property in various derived signed graphs, including the line signed graph, semi-total point signed graph, semi-total line signed graph, and total signed graph. Additionally, we study criticality concepts associated with the restrained domination number in signed graphs. Specifcally, we analyze the efects of removing edges or vertices from signed graphs, as well as adding edges in signed graphs, on the restrained domination number. Further, we extend the concept of restrained domination number to encompass various variants, namely connected restrained domination number, restrained double domination number, and total restrained domination number for signed graphs. We derive relevant results and findings for these parameters, contributing to a deeper understanding of domination in signed graphs.
Edge Domination in Certain Families of Chemical Graphs:
An edge dominating set is a subset of edges of graph such that every edge not in the set is adjacent to an edge in the set. The minimum cardinality taken over all edge dominating sets in the graph G is known as edge domination number.

This concept has attracted several researchers because of its wide applications in different fields such as chemistry, computers and biology. In particular, over the years, it has been a great contribution in the field of chemistry, especially in finding out saturation number of several families of chemical graphs where saturation number for any graph G equals edge domination number. In the present study, we have explored this concept by examining edge domination of few selected class of benzenoid graphs. We have further determined the edge domination number for the system of triangular pericondensed benzenoid graphs. The study also includes some results pertaining to edge domination number of corona product of paths, star and complete graph.
Motivated by the already existing concept of domination subdivision number which equals minimum number of steps required to subdivide any edge of a graph G so as to increase domination number, we define parameters edge domination subdivision number and matching subdivision number. Based on these parameters, we have obtained results for some certain families of graphs and observed that matching subdivision number for any graph is atmost 2 and edge domination subsivision number for some graphs like path, star, cycle, wheel and friendship graph is atmost 3.