Determine Whether Any Two Of $G _ { 1 } , G _ { 2 }$

question 12

Essay

Determine whether any two of $G _ { 1 } , G _ { 2 }$ , and $G _ { 3 }$ are isomorphic. If they are, give vertex and edge functions that define the isomorphism. If they are not, give an isomorphic invariant that they do not share.

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Definitions:

Territoriality

A behavioral pattern in animals where an area is regularly patrolled and defended against intruders, often associated with claiming resources.

Aggregations

Collections or clusters of items, individuals, or particles that come together but are not strictly bound to each other.

Society

A group of individuals belonging to the same species and often closely related; an organized society is an actively cooperating group.

Behavioral Responses

Actions or reactions of an organism in response to external or internal stimuli.