#### Title

Two-Phi-Tolerance Competition Graphs

#### Abbreviated Journal Title

Discret Appl. Math.

#### Keywords

Mathematics, Applied

#### Abstract

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 two-phi-tolerance competition graph is a phi-tolerance competition graph in which all the t(i) are selected from a 2-set. Characterization of such graphs, and relationships between them are presented for phi equal to the minimum, maximum, and sum fractions, with emphasis on the situation in which the 2-set is {0, q}.

#### Journal Title

Discrete Applied Mathematics

#### Volume

66

#### Issue/Number

2

#### Publication Date

1-1-1996

#### Document Type

Article

#### Language

English

#### First Page

101

#### Last Page

108

#### WOS Identifier

#### ISSN

0166-218X

#### Recommended Citation

"Two-Phi-Tolerance Competition Graphs" (1996). *Faculty Bibliography 1990s*. 1560.

https://stars.library.ucf.edu/facultybib1990/1560

## Comments

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