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Turkish Journal of Mathematics

DOI

-

Abstract

In this paper the concept of {\em weak-integrity} is introduced as a new measure of the stability of a graph \( G \) and it is defined as I_{w}(G)={\min_{S\subset V(G)}\{ S +m_{e}(G-S)\}}, where m_{e}(G-S) denotes the number of edges of a largest component of G-S. We investigate the weak-integrity of trees and compute the weak-integrity of a binomial tree and all the trees with at most 7 vertices. We also give some results about the weak-integrity of graphs obtained from binary operations.

First Page

375

Last Page

388

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