An Extremal Problem of Graphs

Yan Jiao

doi:10.47297/wspiedWSP2516-250040.20250901

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Volume 9, Issue 1

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An Extremal Problem of Graphs
An Extremal Problem of Graphs
Department of Basic Courses, Northern Beijing Vocational Education Institute, Beijing, 101400, China
Vol. 9, Issue 1, Pages: 188-192(2025)
Published：20 January 2025
DOI：10.47297/wspiedWSP2516-250040.20250901
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Yan Jiao.An Extremal Problem of Graphs[J].Journal of International Education and Development,2025,09(01):188-192.
DOI：

Yan Jiao.An Extremal Problem of Graphs[J].Journal of International Education and Development,2025,09(01):188-192. DOI： 10.47297/wspiedWSP2516-250040.20250901.

摘要

Abstract

We consider the family of graphs with a fixed number of vertices and edges. Among all these graphs

we determine the minimum of the sum of powers

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=74629666&type=

2.37066650

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1.77800000

of the vertex degrees

for all

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6.34999990

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11.51466751

and characterize the optimal graphs. This solves a problem proposed by Dan Ismailescu and Dan Stefanica.

关键词

Keywords

references

N. Linial , E. Rozenman , An extremal problem on degree sequences of graphs , Graphs and combi . 18 ( 2002 ), 573 - 582 .

M. Talagrand , Isoperimetry , logarithmic Sobolev inequalities on the discrete cube and Margulis' graph connectivity theorem , Geom . Func . Anal . 3 ( 1993 ), no. 3 , 295 - 314 .

D.Ismailescu , D.Stefanica , Minimizer graphs for a class of extremal problems , J. Graph Theory 39 ( 2002 ), 230 - 240 .

V. Chva´tal , P. L. Hammer , Aggregation of inequalities in integer programming , Ann . Discrete Math . 1 ( 1977 ), 145 - 162 .

F. Boetch , R. Brigham , S. Burr , R. Dutton , R. Tindell , Maximizing the Sum of the Squares of the Degrees of a Graph , Tech . Report, Stevens Inst . Tech. , Hoboken , NJ, 1990 .

U.N. Peled , R. Petreschi , A. Sterbini , ( n ; e)-Graphs with Maximum Sum of Squares of Degrees , J. Graph Theory 31 ( 4 ) ( 1999 ), 283 - 295 .

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