Results 41 to 50 of about 445 (75)

Brouwer's conjecture for the sum of the k largest Laplacian eigenvalues of some graphs

Open Mathematics
Let GG be a graph with n(G)n\left(G) vertices and e(G)e\left(G) edges, and Sk(G){S}_{k}\left(G) be the sum of the kk largest Laplacian eigenvalues of GG. Brouwer conjectured that Sk(G)≤e(G)+k+12{S}_{k}\left(G)\le e\left(G)+\left(\phantom{\rule[-0.75em]{}{
Wang Ke, Lin Zhen, Zhang Shumin, Ye Chengfu   +3 more
doaj   +1 more source

Properties of uniformly $3$-connected graphs [PDF]

Discrete Mathematics & Theoretical Computer Science
A graph on at least ${{k+1}}$ vertices is uniformly $k$-connected if each pair of its vertices is connected by $k$ and not more than $k$ independent paths.
Frank Göring, Tobias Hofmann
doaj   +1 more source

ALTERNATING AND SYMMETRIC GROUPS WITH EULERIAN GENERATING GRAPH

Forum of Mathematics, Sigma, 2017
Given a finite group $G$ , the generating graph $\unicode[STIX]{x1D6E4}(G)$
ANDREA LUCCHINI, CLAUDE MARION
doaj   +1 more source

An extremal problem on potentially $K_{m}-P_{k}$-graphic sequences

, 2005
A sequence $S$ is potentially $K_{m}-P_{k}$ graphical if it has a realization containing a $K_{m}-P_{k}$ as a subgraph. Let $\sigma(K_{m}-P_{k}, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $\sigma(S)\geq \sigma(
Lai, Chunhui
core   +1 more source

Complete graphs: the space of simplicial cones, and their path tree representation

, 2017
Let $G$ be a complete graph with $n+1$ vertices. In a recent paper of the authors, it is shown that the path trees of the graph play a special role in the structure of the truncated powers and partition functions that are associated with the graph ...
Ron, Amos, Shengnan, Wang
core  

The Subset-Strong Product of Graphs

Annales Mathematicae Silesianae
In this paper, we introduce the subset-strong product of graphs and give a method for calculating the adjacency spectrum of this product. In addition, exact expressions for the first and second Zagreb indices of the subset-strong products of two graphs ...
Eliasi Mehdi
doaj   +1 more source

On the δ-chromatic numbers of the Cartesian products of graphs

Open Mathematics
In this work, we study the δ\delta -chromatic number of a graph, which is the chromatic number of the δ\delta -complement of a graph. We give a structure of the δ\delta -complements and sharp bounds on the δ\delta -chromatic numbers of the Cartesian ...
Tangjai Wipawee, Pho-on Witsarut, Vichitkunakorn Panupong   +2 more
doaj   +1 more source

On Nordhaus-Gaddum type relations of δ-complement graphs. [PDF]

Heliyon, 2023
Vichitkunakorn P, Maungchang R, Tangjai W.   +2 more
europepmc   +1 more source

Random independent sets in triangle-free graphs

Forum of Mathematics, Sigma
We establish several new results on the existence of probability distributions on the independent sets in triangle-free graphs where each vertex is present with a given probability.
Anders Martinsson, Raphael Steiner
doaj   +1 more source

Steiner Degree Distance of Two Graph Products

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
The degree distance DD(G) of a connected graph G was invented by Dobrynin and Kochetova in 1994. Recently, one of the present authors introduced the concept of k-center Steiner degree distance defined as SDDk(G)=∑S⊆V(G)|S|=k[∑v∈Sdeg⁡G(v)]dG(S),SDD_k (G)
Mao Yaping, Wang Zhao, Das Kinkar Ch.
doaj   +1 more source