Some universal graphs

• Main Authors: Bautista, Paolo Lorenzo Y., Mordeno, Mark Oyelle L.
• Format: text
• Published: Animo Repository 2009
• Subjects: Graph theory; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/faculty_research/11218
• Institution: De La Salle University

Given a graph G with vertex set V (G) = {x1, x2, . . . , xn}, we define the adjacency matrix of G to be the matrix A(G) = [aij ] where aij = 1 if xi and xj are adjacent in G. From the set of all adjacency matrices of G, denoted by A (G), we then form the subspace spanned by this set, denoted by (A (G)). A graph with adjacency matrix H is said to be a G-descendant if H ∈ (A (G)). If G is of order n and all graphs of order n are G-descendants, we say that G is universal. In this paper, we show that complements of some universal graphs are also universal.