Results 11 to 20 of about 3,067,250 (321)
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
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
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
Some new results on sum index and difference index
AIMS Mathematics, 2023 Let $ G = (V(G), E(G)) $ be a graph with a vertex set $ V(G) $ and an edge set $ E(G) $. For every injective vertex labeling $ f:V\left (G \right)\to \mathbb{Z} $, there are two induced edge labelings denoted by $ f^{+} :E\left (G \right)\to \mathbb{Z} $
Yuan Zhang, Haiying Wang
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 +8 more sources
Optimization over Degree Sequences [PDF]
SIAM Journal on Discrete Mathematics, 2018 We introduce and study the problem of optimizing arbitrary functions over degree sequences of hypergraphs and multihypergraphs. We show that over multihypergraphs the problem can be solved in polynomial time. For hypergraphs, we show that deciding if a given sequence is the degree sequence of a 3-hypergraph is NP-complete, thereby solving a 30 year ...
Deza, Antoine +3 more
openaire +2 more sources
A Degree Sequence Komlós Theorem [PDF]
SIAM Journal on Discrete Mathematics, 2019 20 pages, 4 figures. Author accepted manuscript.
Joseph Hyde, Hong Liu, Andrew Treglown
openaire +2 more sources
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
The irregularity of two types of trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 The irregularity of a graph $G$ is defined as the sum of weights $|d(u)-d(v)|$ of all edges $uv$ of $G$, where $d(u)$ and $d(v)$ are the degrees of the vertices $u$ and $v$ in $G$, respectively.
Li Jianxi, Yang Liu, Wai Shiu
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