A Zero of Maximum Multiplicity

SIAM Review ◽  
1976 ◽  
Vol 18 (4) ◽  
pp. 763-763
Author(s):  
N. Liron
Keyword(s):  
Maximum Multiplicity

scholarly journals The trees for which maximum multiplicity implies the simplicity of other eigenvalues

2006 ◽  
Vol 306 (23) ◽  
pp. 3130-3135
Author(s):  
Charles R. Johnson ◽  
Carlos M. Saiago
Keyword(s):  
Maximum Multiplicity

scholarly journals Reaching the Maximum Multiplicity of the Covalent Chemical Bond

2007 ◽  
Vol 119 (9) ◽  
pp. 1491-1494 ◽  
Author(s):  
Björn O. Roos ◽  
Antonio C. Borin ◽  
Laura Gagliardi
Keyword(s):  
Chemical Bond ◽  
Covalent Chemical Bond ◽  
Maximum Multiplicity

scholarly journals A Note on Repeated Degrees of Line Graphs

10.37236/9608 ◽  
2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Shimon Kogan
Keyword(s):  
Line Graph ◽  
Vertex Degree ◽  
Line Graphs ◽  
Maximum Multiplicity

Let $\text{rep}(G)$ be the maximum multiplicity of a vertex degree in graph $G$. It was proven in Caro and West [E-JC, 2009] that if $G$ is an $n$-vertex line graph, then $\text{rep}(G) \geqslant \frac{1}{4} n^{1/3}$. In this note we prove that for infinitely many $n$ there is a $n$-vertex line graph $G$ such that $\text{rep}(G) \leqslant \left(2n\right)^{1/3}$, thus showing that the bound above is asymptotically tight. Previously it was only known that for infinitely many $n$ there is a $n$-vertex line graph $G$ such that $\text{rep}(G) \leqslant \sqrt{4n/3}$ (Caro and West [E-JC, 2009]). Finally we prove that if $G$ is a $n$-vertex line graph, then $\text{rep}(G) \geqslant \left(\left(\frac{1}{2}-o(1)\right)n\right)^{1/3}$.

A Zero Of Maximum Multiplicity (N. Liron and L. A. Rubenfeld)

SIAM Review ◽  
1977 ◽  
Vol 19 (4) ◽  
pp. 743-744
Author(s):  
w. B. Jordan
Keyword(s):  
Maximum Multiplicity

Onn-Sums in an Abelian Group

2015 ◽  
Vol 25 (3) ◽  
pp. 419-435 ◽  
Author(s):  
WEIDONG GAO ◽  
DAVID J. GRYNKIEWICZ ◽  
XINGWU XIA
Keyword(s):  
Abelian Group ◽  
Maximum Multiplicity

LetGbe an additive abelian group, letn⩾ 1 be an integer, letSbe a sequence overGof length |S| ⩾n+ 1, and let${\mathsf h}$(S) denote the maximum multiplicity of a term inS. Let Σn(S) denote the set consisting of all elements inGwhich can be expressed as the sum of terms from a subsequence ofShaving lengthn. In this paper, we prove that eitherng∈ Σn(S) for every termginSwhose multiplicity is at least${\mathsf h}$(S) − 1 or |Σn(S)| ⩾ min{n+ 1, |S| −n+ | supp (S)| − 1}, where |supp(S)| denotes the number of distinct terms that occur inS. WhenGis finite cyclic andn= |G|, this confirms a conjecture of Y. O. Hamidoune from 2003.

scholarly journals The graphs for which the maximum multiplicity of an eigenvalue is two

2009 ◽  
Vol 57 (7) ◽  
pp. 713-736 ◽  
Author(s):  
Charles R. Johnson ◽  
Raphael Loewy ◽  
Paul Anthony Smith
Keyword(s):  
Maximum Multiplicity ◽  
Multiplicity Of An Eigenvalue
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