On the Range of Possible Integrities of Graphs G(n, k) |
| |
Authors: | Mustafa Atici Claus Ernst |
| |
Institution: | 1. Department of Mathematics and Computer Science, Western Kentucky University, Bowling Green, KY, 42101, USA
|
| |
Abstract: | We discuss the range of values for the integrity of a graphs G(n, k) where G(n, k) denotes a simple graph with n vertices and k edges. Let I
max(n, k) and I
min(n, k) be the maximal and minimal value for the integrity of all possible G(n, k) graphs and let the difference be D(n, k) = I
max(n, k) − I
min(n, k). In this paper we give some exact values and several lower bounds of D(n, k) for various values of n and k. For some special values of n and for s < n
1/4 we construct examples of graphs G
n
= G
n
(n, n + s) with a maximal integrity of I(G
n
) = I(C
n
) + s where C
n
is the cycle with n vertices. We show that for k = n
2/6 the value of D(n, n
2/6) is at least
\frac?6-13n{\frac{\sqrt{6}-1}{3}n} for large n. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|