Suppose a biking environment consists of n ≥ 3 landmarks, which are linked by bike route in a cyclical manner. That is, there is a bike route between landmark 1 and 2, between landmark 2 and 3, and so on until we link landmark n back to landmark 1. In the center of these is a mountain which has a bike route to every single landmark. Besides these, there are no other bike routes in the biking environment. You can think of the landmarks and the single mountain as nodes, and the bike routes as edges, which altogether form a graph G. A path is a sequence of bike routes. What is the number of paths of length 2 in the graph in terms of n? What is the number of cycles of length 3 in the graph in terms of n? What is the number of cycles in the graph in terms of n?
Suppose a biking environment consists of n ≥ 3 landmarks, which are linked by bike route in a cyclical manner. That is, there is a bike route between landmark 1 and 2, between landmark 2 and 3, and so on until we link landmark n back to landmark 1. In the center of these is a mountain which has a bike route to every single landmark. Besides these, there are no other bike routes in the biking environment. You can think of the landmarks and the single mountain as nodes, and the bike routes as edges, which altogether form a graph G. A path is a sequence of bike routes. What is the number of paths of length 2 in the graph in terms of n? What is the number of cycles of length 3 in the graph in terms of n? What is the number of cycles in the graph in terms of n?
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Suppose a biking environment consists of n ≥ 3 landmarks,
which are linked by bike route in a cyclical manner. That is, there
is a bike route between landmark 1 and 2, between landmark 2 and 3,
and so on until we link landmark n back to landmark 1. In the center
of these is a mountain which has a bike route to every single landmark.
Besides these, there are no other bike routes in the biking environment.
You can think of the landmarks and the single mountain as nodes, and
the bike routes as edges, which altogether form a graph G. A path is a
sequence of bike routes.
What is the number of paths of length 2 in the graph in terms
of n?
What is the number of cycles of length 3 in the graph in terms
of n?
What is the number of cycles in the graph in terms of n?
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