Bibliographic Details
| Title: |
Exact and approximate results on the least size of a graph with a given degree set. |
| Authors: |
Moondra, Jai1 (AUTHOR) jmoondra3@gatech.edu, Sahdev, Aditya1,2 (AUTHOR) aditya.sahdev@alumni.iitd.ac.in, Tripathi, Amitabha1,3 (AUTHOR) atripath@maths.iitd.ac.in |
| Source: |
Discrete Applied Mathematics. Jul2023, Vol. 333, p32-42. 11p. |
| Abstract: |
The degree set of a finite simple graph G is the set of distinct degrees of vertices of G. A theorem of Kapoor, Polimeni & Wall asserts that the least order of a graph with a given degree set D is 1 + max D. Tripathi & Vijay considered the analogous problem concerning the least size of graphs with degree set D. We expand on their results, and determine the least size of graphs with degree set D when (i) min D divides d for each d ∈ D ; (ii) min D = 2 ; (iii) D = { m , m + 1 , ... , n }. In addition, given any D , we produce a graph G whose size is within min D of the optimal size, giving a (1 + 2 d 1 + 1) -approximation, where d 1 = max D. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
