Results 11 to 20 of about 2,991,925 (319)
Graphs with Given Degree Sequence and Maximal Spectral Radius [PDF]
, 2008 We describe the structure of those graphs that have largest spectral radius in the class of all connected graphs with a given degree sequence. We show that in such a graph the degree sequence is non-increasing with respect to an ordering of the vertices ...
Türker Bı́yı́koğlu, Josef Leydold
openalex +5 more sources
Mathematics, 2022 Let G(V,X) be a finite and simple graph of order n and size m. The complement of G, denoted by G¯, is the graph obtained by removing the lines of G and adding the lines that are not in G.
Amrithalakshmi Pai +4 more
doaj +1 more source
The degree sequence on tensor and cartesian products of graphs and their omega index
AIMS Mathematics, 2023 The aim of this paper is to illustrate how degree sequences may successfully be used over some graph products. Moreover, by taking into account the degree sequence, we will expose some new distinguishing results on special graph products.
Bao-Hua Xing +2 more
doaj +1 more source
The degree of asymmetry of sequences
Enumerative Combinatorics and Applications, 2021 We explore the notion of degree of asymmetry for integer sequences and related combinatorial objects. The degree of asymmetry is a new combinatorial statistic that measures how far an object is from being symmetric. We define this notion for compositions, words, matchings, binary trees and permutations, we find generating functions enumerating these ...
Sergi Elizalde, Emeric Deutsch
openaire +3 more sources
Largest Laplacian Eigenvalue and Degree Sequences of Trees [PDF]
, 2008 We investigate the structure of trees that have greatest maximum eigenvalue among all trees with a given degree sequence. We show that in such an extremal tree the degree sequence is non-increasing with respect to an ordering of the vertices that is ...
Tuerker Biyikoglu +2 more
openalex +4 more sources
An extremal problem on potentially K_p,1,1-graphic sequences [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 A sequence S is potentially K_p,1,1 graphical if it has a realization containing a K_p,1,1 as a subgraph, where K_p,1,1 is a complete 3-partite graph with partition sizes p,1,1.
Chunhui Lai
doaj +1 more source
The Random Plots Graph Generation Model for Studying Systems with Unknown Connection Structures
Entropy, 2022 We consider the problem of modeling complex systems where little or nothing is known about the structure of the connections between the elements. In particular, when such systems are to be modeled by graphs, it is unclear what vertex degree distributions
Evgeny Ivanko, Mikhail Chernoskutov
doaj +1 more source
Packing Tree Degree Sequences [PDF]
Graphs and Combinatorics, 2019 AbstractA degree sequence is a list of non-negative integers, $${D = d_1, d_2, \ldots , d_n}$$D=d1,d2,…,dn. It is called graphical if there exists a simple graph G such that the degree of the ith vertex is $$d_i$$di; G is then said to be a realization of D. A tree degree sequence is one that is realized by a tree.
Bérczi, Kristóf +3 more
openaire +9 more sources
A General Computational Approach for Counting Labeled Graphs
Algorithms, 2022 This paper presents a general recursive formula to estimate the number of labeled graphs as well as details to evaluate the formula for the following graph properties: number of edges (graph density), degree sequence, degree distribution, classification ...
Ravi Goyal, Victor De Gruttola
doaj +1 more source
On degree sequence optimization [PDF]
Operations Research Letters, 2020 We consider the problem of finding a subgraph of a given graph which maximizes a given function evaluated at its degree sequence. While the problem is intractable already for convex functions, we show that it can be solved in polynomial time for convex multi-criteria objectives.
openaire +3 more sources