On Radio Labeling of Diameter N-2 and Caterpillar Graphs

Abstract

determined the radio number of complete m-ary trees [7]. Ruxandra Marinescu-Ghemeci found the radio number for some thorn graphs, one of which is a particular type of caterpillar graph [10]. This thesis builds off of work done on paths and trees in general to determine an improved lower bound or the actual radio number of certain types of caterpillar graphs. This thesis includes joint work with Matthew Porter and Maggy Tomova on determining the radio numbers of graphs with n vertices and diameter n − 2, a subcase of which is a particular caterpillar. This thesis also establishes the radio number of some specific caterpillar graphs as well as an improved lower bound for the radio number of more general caterpillar graphs. v TABLE OF CONTENTS LIST OF TABLES .