Results 21 to 30 of about 2,991,925 (319)
Symmetric bipartite graphs and graphs with loops [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Graph ...
Grant Cairns, Stacey Mendan
doaj +1 more source
On the Grone-Merris conjecture [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Grone and Merris [GM94] conjectured that the Laplacian spectrum of a graph is majorized by its conjugate vertex degree sequence. We prove that this conjecture holds for a class of graphs including trees.
Tamon Stephen
doaj +1 more source
Spectral ordering and 2-switch transformations [PDF]
The American Journal of Combinatorics, 2022 We address the problem of ordering trees with the same degree sequence by their spectral radii. To achieve that, we consider 2-switch transformations which preserve the degree sequence and establish when the index decreases.
Elismar Oliveira +2 more
doaj +3 more sources
On factorable degree sequences
Journal of Combinatorial Theory, Series B, 1972 AbstractWe call a degree sequence graphic (respectively, k-factorable, connected k-factorable) if there exists a graph (respectively, a graph with a k-factor, a graph with a connected k-factor) with the given degree sequence. In this paper we give a necessary and sufficient condition for a k-factorable sequence to be connected k-factorable when k ⩾ 2 ...
A Ramachandra Rao, S.B Rao
openaire +2 more sources
An inequality for degree sequences
Discrete Mathematics, 1992 The authors prove that \[ \left(\sum^ n_{i=1} d^{1/p}_ i\right)^ p\geq \sum^ n_{i=1} d^ p_ i \] for the degree sequence \(d_ 1,\dots,d_ n\) of a simple graph and \(p\) a positive integer. Moreover, they analyze also related ``real'' inequalities. Some partial results are interesting for their own sake, e.g.
L. H. Clark +2 more
openaire +3 more sources
Enumeration of graphs with a heavy-tailed degree sequence [PDF]
, 2016 In this paper, we asymptotically enumerate graphs with a given degree sequence d=(d_1,...,d_n) satisfying restrictions designed to permit heavy-tailed sequences in the sparse case (i.e. where the average degree is rather small).
Gao, Pu, Wormald, Nicholas
core +1 more source
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
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
On the reconstruction of the degree sequence
Discrete Mathematics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dieter Rautenbach +2 more
openaire +3 more sources
On degree-sequence characterization and the extremal number of edges for various Hamiltonian properties under fault tolerance [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 Assume that $n, \delta ,k$ are integers with $0 \leq k < \delta < n$. Given a graph $G=(V,E)$ with $|V|=n$. The symbol $G-F, F \subseteq V$, denotes the graph with $V(G-F)=V-F$, and $E(G-F)$ obtained by $E$ after deleting the edges with at least one ...
Shih-Yan Chen, Shin-Shin Kao, Hsun Su
doaj +1 more source