“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 8726
School of Mathematics
  Title:   Some relations between rank, chromatic number and energy of graphs
  Author(s): 
1.  S. Akbari
2.  E. Ghorbani (Joint with S. Zare)
  Status:   To Appear
  Journal: Discrete Math.
  Supported by:  IPM
  Abstract:
The energy of a graph G, denoted by E(G), is defined as the sum of the absolute values of all eigenvalues of G. Let G be a graph of order n and rank (G) be the rank of the adjacency matrix of G. In this paper we characterize all graphs with E(G) = rank(G). Among other results we show that apart from a few families of graphs, E(G) ≥ 2max(X(G),nX(G), where n is the number of vertices of G, G and X(G) are the complement and the chromatic number of G, respectively. Moreover some new lower bounds for E(G) in terms of rank (G) are given.

Download TeX format
back to top
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
scroll left or right