#### Title

Tolerance Competition Graphs

#### Abbreviated Journal Title

Linear Alg. Appl.

#### Keywords

Mathematics, Applied; Mathematics

#### Abstract

The phi-tolerance competition graph is introduced as a generalization of the p-competition graphs defined by Kim, McKee, McMorris, and Roberts. Let phi be a symmetric function defined from N x N into N, where N denotes the nonnegative integers. G = (V, E) is a phi-tolerance competition graph if there is a directed graph D = (V, A) and an assignment of a nonnegative integer t(i) to each vertex v(i) is an element of V such that, for i not equal j, v(i)v(j) is an element of E(G) if and only if \O(v(i)) boolean AND O(v(j))\ greater than or equal to phi(t(i),t(j)), where O(x) = {y : xy is an element of A}. A general characterization of phi-tolerance competition graphs is given, and specific results are obtained when phi is the minimum, maximum, and sum functions.

#### Journal Title

Linear Algebra and Its Applications

#### Volume

217

#### Publication Date

1-1-1995

#### Document Type

Article; Proceedings Paper

#### Language

English

#### First Page

41

#### Last Page

52

#### WOS Identifier

#### ISSN

0024-3795

#### Recommended Citation

"Tolerance Competition Graphs" (1995). *Faculty Bibliography 1990s*. 1292.

https://stars.library.ucf.edu/facultybib1990/1292

## Comments

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