On the least size of a graph with a given degree set
نویسندگان
چکیده
منابع مشابه
On the least size of a graph with a given degree set
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). We look at the analogous problem concerning the least size of a graph with a given degree set D. We determine the least size for the sets D when (i) |D| ≤ 3; (ii) D = {1, 2, . . . , n}; an...
متن کاملEla a Note on the Least Eigenvalue of a Graph with given Maximum Degree
This note investigates the least eigenvalues of connected graphs with n vertices and maximum degree ∆, and characterizes the unique graph whose least eigenvalue achieves the minimum among all the connected graphs with n vertices and maximum vertex degree ∆ > n 2 .
متن کاملDiameter Two Graphs of Minimum Order with Given Degree Set
The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...
متن کاملA note on the least eigenvalue of a graph with given maximum degree
This note investigates the least eigenvalues of connected graphs with n vertices and maximum degree ∆, and characterizes the unique graph whose least eigenvalue achieves the minimum among all the connected graphs with n vertices and maximum vertex degree ∆ > n 2 .
متن کاملThe Size of the Giant Component of a Random Graph with a Given Degree Sequence
Given a sequence of non negative real numbers which sum to we consider a random graph having approximately in ver tices of degree i In the authors essentially show that if P i i i then the graph a s has a giant component while if P i i i then a s all components in the graph are small In this paper we analyze the size of the giant component in the former case and the structure of the graph forme...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2006
ISSN: 0166-218X
DOI: 10.1016/j.dam.2006.04.003