Integrity and vertex neighbor integrity of some graphs

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DOI:

https://doi.org/10.26637/mjm1103/004

Abstract

The integrity I(G) of a noncomplete connected graph G is a measure of network vulnerability and is defined by I(G)=minSV(G){|S|+m(GS)}, where S and m(GS) denote the subset of V and the order of the largest component of GS, respectively. The vertex neigbor integrity denoted as VNI(G) is the concept of the integrity of a connected graph G and is defined by VNI(G)=minSV(G){|S|+m(GS)}, where S is any vertex subversion strategy of G and m(GS) is the number of vertices in the largest component of GS. If a network is modelled as a graph, then the integrity number shows not only the difficulty to break down the network but also the damage that has been caused. This article includes several results on the integrity of the k-ary treeHkn, the diamond-necklace Nk, the diamond-chain Lk and the thorn graph of the cycle graph and the vertex neighbor integrity of the H2n, H3n.

Keywords:

Integrity, vertex neighbor integrity, vulnerability

Mathematics Subject Classification:

03D20, 05C07, 05C69, 68M10
  • Pages: 278-285
  • Date Published: 01-07-2023
  • Vol. 11 No. 03 (2023): Malaya Journal of Matematik (MJM)

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Published

01-07-2023

How to Cite

ATAY ATAKUL, betül. “Integrity and Vertex Neighbor Integrity of Some Graphs”. Malaya Journal of Matematik, vol. 11, no. 03, July 2023, pp. 278-85, doi:10.26637/mjm1103/004.