Research trends in graph theory and applications The Workshop for Women in Graph Theory and Applications was held at the Institute for Mathematics and Its Applications (University of Minnesota Minneapolis) on August 19 23 2019. During this five day workshop 42 participants performed collaborative research in six teams each focused on open problems in different areas of graph theory and its applications. The research work of each team was led by two experts in the corresponding area who prior to the workshop carefully selected relevant and meaningful open problems that would yield high quality research and results of strong impact. As a result all six teams have made significant contributions to several open problems in their respective areas. The workshop led to the creation of the Women in Graph Theory and Applications Research Network which provided the framework to continue collaborating and to produce this volume. This book contains six chapters each of them on one of the different areas of research at the Workshop for Women in Graph Theory and Applications and written by participants of each team. Finding Long Cycles in Balanced Tripartite Graphs: A First Step (L. Lesniak) Product Thottling (L.Hogben) Analysis of Termatiko Sets in Measurement Matrices (L. Matthews) The Threshold Dimension and Threshold Strong Dimension of a Graph: A Survey (O. Oellermann) Symmetry Parameters for Mycielskian Graphs (D. Boutin) Reconfiguration Graphs for Dominating Sets (R. Haas).