2017/08/07 by Niran Abbas Ali, Gek L. Chiab, Ali, Niran Abbas +5
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1708.02024
openalex publication_date 2017/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A well known Euler's formula consequence's corollary in graph theory states\nthat: For a connected simple planar graph with n vertices and m edges, and\ngirth g, we have m \≤ \(g)/(g-2)(n-2). We show that a connected simple\nplane graph with n vertices and girth g, and exterior face of degree h\nhas at most \(g)/(g-2)(n-2)- \(1)/(g-2)(h-g) edges. A \convex hull\ng-angulation is a connected plane graph in which the exterior face is a\nsimple h-cycle and all inner faces are g-cycles. For a given set S of n\npoint in the plane having h points in the boundary of its convex hull, we\npresent the necessary and sufficient condition to obtain a convex hull\ng-angulation on S. We also determine the number of edges and inner faces in\nthe convex hull g-angulation.\n