Asian Journal of Mathematics and Computer Research
 

Asian Journal of Mathematics and Computer Research, ISSN No. : 2395-4205 (Print), 2395-4213 (Online), Vol.: 22, Issue.: 4

Short Research Article

EIGENVALUES AND HAMILTONICITY OF QUASI - CLAW - FREE GRAPHS

 

RAO LI1*
1Department of Mathematical Sciences, University of South Carolina Aiken, Aiken, SC 29801, South Carolina, USA.

Abstracts

A graph is quasi - claw - free if it satisfies the property: d(x, y) = 2 ⇒ there exists uN(x)∩N(y) such that N[u] ⊆ N[x]∪[N[y]. Let G be a k - connected quasi - claw - free graph. Using eigenvalues of G or eigenvalues of the complement of G, we in this note present sufficient conditions for the Hamiltonicity of G.

Keywords :

Eigenvalue; hamiltonicity; quasi-claw-free; graph.