Zingiswa Jojo is a full professor in the department of Mathematics Education at
UNISA. She is a scholar who serves as the local organizing committee of AMESA,
the Commission for African Women in Mathematics (AMU-CAWM), an academic
board member in the Athens Institute for Education and Research, and a leader of
several projects aimed at promoting Mathematics teaching and learning. Zingiswa
holds a PhD in Mathematics Education from the University of KwaZulu Natal. She
has published and presented numerous papers, hosted in some leading universities
located in countries like Umea in Sweden, Rio de Janeiro in Brazil, Athens in
Greece, Dublin in Ireland, e-Learning in Kigali, Rwanda and PACOM in Congo
Brazzaville.

Consider a graph \(G(V, E)\). A function \(\pi:V\rightarrow\{1, \ldots, k\}\) is a packing coloring of order \(k\) if \(\pi(u) = \pi(v)\) implies the distance between \(u\) and \(v\) is more than \(\pi(u)\). The minimum number of colors with which the vertices of a graph \(G\) can be packing colored is called the packing chromatic number of \(G\), denoted by \(\chi_\rho(G)\). We will discuss the packing chromatic number of various graphs with emphasis on the upper bound and the lower bound of the packing chromatic number of the 2- dimensional infinite square lattice/grid. A discussion of the packing chromatic number of the torus will follow. A comparison will be made between the packing chromatic numbers of the grid and the torus.

**References**

[1] A survey on packing colorings, B Bresar, J Ferme, S Klavzar, D F Rall, Discussiones Mathematicae Graph Theory 40, 2020, 923-970

Betsie did her undergraduate studies at UP; her graduate Studies at UJ (RAU). She taught at High School Die Fakkel (1980 – 1992) and was a lecturer/senior lecturer and associate professor at UJ (RAU) (1993 – 2016). From 2016 until now, she is employed at Wits. Betsie was HoS/Deputy HoS of Mathematics at UJ and then at Wits (18 years in total). She became full professor in March 2019.

Betsie published 23 ISI articles, supervised/co-supervised to completion 7 doctoral and 15 masters students. She presented at 32 conferences, here and overseas. She externals for universities and evaluated 7 times other schools/departments of mathematics at universities in the country.

(Nelson Mandela University and La Trobe University)

Professor Weideman graduated from the University of the Free state in 1986, and occupied positions at that university and at Oregon State University, as well as visiting positions at MIT and the University of Utah. He is currently Distinguished Professor of Applied Mathematics at Stellenbosch University.