Graphs are everywhere in mathematics if only we know how to identify these structures. The theory of graphs and the theory of knots have enjoyed a symbiotic relationship since the inception of knot theory. In this talk, we give a formal definition of a graph followed by a few examples. We also give a formal definition of a knot followed by a few examples. Thereafter, we discuss the basic relationship between a graph and a knot. Furthermore, we give one example of how the theory of knots has benefited from the theory of graphs.
1] C.C. Adams, The knot book, W.H.Freeman and Company, New York, (1994).
 L.H. Kauffman, New invariants in the theory of knots, The American Mathematical Monthly 95 (1988) 195–242.
 E.G. Mphako, The component number of links from graphs Proceedings of the Edinburgh Mathematical Society 45 (2002) 723–730.
 W. Tutte, Graph Theory as I Have Known It, Oxford Univeristy Press, Oxford,(1998).
Short biography of Speaker:
Eunice Gogo Mphako-Banda was born in Blantyre, Malawi. She graduated from the University of Malawi with a B.Ed. in sciences in 1992. This was followed by a Postgraduate Diploma in Mathematics from the University of Sheffield, UK, in 1994, an MSc in Mathematics from the University of Manchester, UK, in 1995, and a Ph.D. in Discrete Mathematics from Victoria University of Wellington, New Zealand in 2001. She was a recipient of the UNIMA Scholarship for girls in sciences from 1988 -1991, the British Council Scholarship in 1994 and 1995, and the New Zealand Overseas Development Scholarship in 1998.
Her academic career started at the Department of Mathematical Sciences, the University of Malawi in 1993 as Associate Lecturer where she eventually rose to the rank of Senior Lecturer and in 2003 became the Head of School. She joined the University of KwaZulu-Natal, School of Mathematical Sciences in 2007 as a Lecturer. In September 2008, she joined the University of the Witwatersrand, School of Mathematics as a Lecturer, became a Senior Lecturer in December 2011, Associate Professor in December 2013, and Professor in March 2019.
Her current research interests include Matroid Theory, Low- Dimension Topology-Knot Theory, Combinatorics, and Graph Theory. Her research in Matroid Theory is focused on matroid construction and polynomials. In Knot Theory, her interest varies from knot invariants to knot construction. She uses Combinatorics and Graph Theory as tools to solving problems in Matroid Theory and Knot Theory.
Prof Mphako-Banda is actively serving as a representative of SAMS in ICIAM Board, a member of the grant selection committee in IMU, and the liaison officer of SAMS. She is also a member of many Professional Bodies, namely: SAMSA, SAWISE, SAWMSA, SAMS, and AMU.