A Note on Angular Geometric Graphs

Abstract

In this short note we first define angular geometric graphs, angular degrees and geometric degrees in graph theory as follows. An angular geometric graph denoted as AGG is a graph in which given angles between vertices and edges can not be changed. If the angles are not given specifically in an angular geometric graph, all the angles are considered to be equal. The sum of the sines of the all angles of a vertex v is called the angular degree of v and denoted as ang(v). The sum of the degree of the vertex v and the angle degree of the vertex v is called the geometric degree of v and denoted as geom(v). The aim of this study is to investigate the geometric degrees of the Cartesian product of two paths and a path with a cycle.