Question

Suppose that a new company has five employees: Zamora, Agraharam, Smith, Chou, and Macintyre. Each employee will assume one of six responsibilities: planning, publicity, sales, marketing, development, and industry relations. Each employee is capable of doing one or more of these jobs: Zamora could do planning, sales, marketing, or industry relations; Agraharam could do planning or development; Smith could do publicity, sales, or industry relations; Chou could do planning, sales, or industry relations; and Macintyre could do planning, publicity, sales, or industry relations. Model the capabilities of these employees using a bipartite graph.

Answer 1

Following are the possible responsibilities of each of the five employees;

Zamora: Planning, Sales, Marketing, Industry relations

Agraharam: Planning, Development

Smith: Publicity, Sales, Industry relations

Chou: Publicity, Sales, Industry relations

Macintyre: Planning, Publicity, Sales, Industry relation

The vertices are the five employees and the six responsibilities areas. There is an edge between an employee and a responsibility, if the employee could execute the responsibility.

`T_(1)` = {Zamora, Agraharam, Smith, Chou, Macintyre}

`T_(2)`= {Planning, Publicity, Sales, Marketing, Development, Industry relations}

E = {(Zamora, Planning), (Zamora, Sales), (Zamora, Marketing), (Zamora, Industry relations), (Agraharam, Planning), (Agraham, Development), (Smith, Sales), (Smith, Publicity), (Smith, Industry relations) (Chou, Sales), (Chou, Publicity), (Chou, Industry relations), (Macintyre, Planning), (Macintyre, Sales), (Macintyre, Publicity), (Macintyre, Industry relations)}

Explanation:

a bipartite graph is a simple graph whose vertices can be partitioned into two sets
`T_(1)` and
`T_(2)` such that there are no edges among the vertices of
`T_(1)` and no edges among the vertices of
`T_(2)`, while there can be edges between a vertex of
`T_(1)` and a vertex of
`T_(2)`

Answer 2

Explanation:

Before constructing bipartite graph, we need to have the responsibilities of each person sorted out first. I listed it in dash form for easy reading

Zamora

- planning,

- sales, marketing

- industry relations

Agraharam:

- planning

- development

Smith

- publicity,

- sales,

- industry relations

Chou

- planning,

- sales,

- industry relations

Macintyre

- planning,

- publicity,

- sales,

- industry relations

After we are done with that, we can start constructing the bipartite graph by making two column or two rows of group, one is for the person and the other is for responsibilities.

Later, we start match up each person to the responsibilities that assigned to them.

I attached the bipartite graph for this question as well.