# A First Course in Graph Theory and CombinatoricsRecurrence Relations

A First Course in Graph Theory and Combinatorics: Recurrence Relations [Combinatorics is the study of finite sets. To define finite sets, we need the notion of bijective function. Given two sets X and Y, a function f : X → Y is injective or one-to-one if f(a) ≠ f(b) for any a, b ∈ X with a ≠ b. A function f : X → Y is surjective or onto if for any y ∈ Y, there exist x ∈ X such that f(x) = y. A function is bijective if it is injective and surjective. A function f : X → Y is invertible if there exists a function g : Y → X such that f(x) = y if and only if g(y) = x. If g exists, it is called the inverse of f and it is usually denoted by f−1. We leave as an exercise the fact that a function is bijective if and only if it is invertible.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A First Course in Graph Theory and CombinatoricsRecurrence Relations

Part of the Texts and Readings in Mathematics Book Series (volume 55)
Springer Journals — May 24, 2017
13 pages      /lp/springer-journals/a-first-course-in-graph-theory-and-combinatorics-recurrence-relations-NWs039C2Ov
Publisher
Hindustan Book Agency
© Hindustan Book Agency (India) 2009
ISBN
978-81-85931-98-2
Pages
10 –23
DOI
10.1007/978-93-86279-39-2_2
Publisher site
See Chapter on Publisher Site

### Abstract

[Combinatorics is the study of finite sets. To define finite sets, we need the notion of bijective function. Given two sets X and Y, a function f : X → Y is injective or one-to-one if f(a) ≠ f(b) for any a, b ∈ X with a ≠ b. A function f : X → Y is surjective or onto if for any y ∈ Y, there exist x ∈ X such that f(x) = y. A function is bijective if it is injective and surjective. A function f : X → Y is invertible if there exists a function g : Y → X such that f(x) = y if and only if g(y) = x. If g exists, it is called the inverse of f and it is usually denoted by f−1. We leave as an exercise the fact that a function is bijective if and only if it is invertible.]

Published: May 24, 2017