## Honors College Capstone Experience/Thesis Projects

#### Department

Computer Science

#### Document Type

Thesis

#### Abstract

Integrity of a graph is defined as ๐บ = ๐๐๐๐โ๐(๐บ){ ๐ + ๐ ๐บ โ ๐ } , where G is a graph with vertex set V and m(G-S) denotes the order of the largest component of G - S. This provides an upper estimate of the integrity of the given graph. Using graph coloring, the color sequence of the graph can be generated, with the leading term being the largest component of the graph, the maximal independent set. The determination of the set is too time intensive to be feasible for moderate to large graphs, since there is no polynomial time algorithm to do so. My algorithm completes this task with reasonable accuracy within O(N2) time. This allows for generation of an upper bound of integrity, and an estimation of real integrity, for even extremely large graphs. With integrity known or estimated, network reliability can be estimated based on their topography. Through comparison of different potential network architectures, network engineers may construct stronger networks based on which network has a higher integrity.

#### Advisor(s) or Committee Chair

Dr. Mustafa Atici

#### Disciplines

Computer Engineering

#### Recommended Citation

Burchett, Ian, "Quantifying Network Reliability Through Finding An Upper Bound For Graph Integrity Using Graph Coloring" (2009). *Honors College Capstone Experience/Thesis Projects.* Paper 225.

http://digitalcommons.wku.edu/stu_hon_theses/225