Results 21 to 30 of about 405,795 (217)

On dynamic colouring of cartesian product of complete graph with some graphs

Journal of Taibah University for Science, 2020
A proper vertex colouring is called a 2-dynamic colouring, if for every vertex v with degree at least 2, the neighbours of v receive at least two colours. The smallest integer k such that G has a dynamic colouring with k colours denoted by $\chi _2(G) $.
K. Kaliraj, H. Naresh Kumar, J. Vernold Vivin   +2 more
doaj   +1 more source

Completely connected clustered graphs

Journal of Discrete Algorithms, 2003
A clustered graph \((G,T,r)\) consists of a graph \(G=(V,E)\), a tree \(T\), and an inner vertex \(r\) of \(T\) such that the set of leaves of \(T\) is exactly \(V\). A clustered graph is said to be completely connected if every cluster, and also each complement of a cluster, induces a connected subgraph.
Cornelsen, Sabine, Wagner, Dorothea
openaire   +2 more sources

On Some Properties of Characteristics Polynomials of the Complete Graphs Kn [PDF]

Engineering and Technology Journal, 2013
This paper discusses the properties of the characteristic polynomial of the complete graphs Kn, n=1, 2… respective to the adjacency matrices. Two different types of matrices, the adjacency matrix and the signless Laplacian matrix, are presented.
Nuha A. Rajab, Samaa F. Ibraheem, Eman H. Ouda   +2 more
doaj   +1 more source

When Is a Graded Free Complex Exact?

Mathematics, 2022
Minimal free resolutions of a finitely generated module over a polynomial ring S=k[x], with variables x={x1,…,xn} and a field k have been extensively studied.
David C. Molano, Javier A. Moreno, Carlos E. Valencia   +2 more
doaj   +1 more source

Teorema Pohon Matriks Untuk Menentukan Banyaknya Pohon Rentangan Graf Bipartisi Komplit (Km,n)

Fokus, 2016
This research aims to observes panning tree number of complete bipartite graph (Km,n) by matrix-tree theorem.This research was using library research method which the step are:(1)Drawing complete bipartite graph (Km,n) where m= 1,2,3,4,and; (2)Determinin
Novia Rahmawati
doaj   +1 more source

The Reliability of a Class of Two-Layer Networks with Unreliable Edges

Axioms
It is well known that networks are dynamic graphs, and the topology of a network can be described by a graph. Thus, the reliability of a network under edge failure is defined as the probability that its corresponding topological graph remains connected ...
Sun Xie, Haixing Zhao, Jun Yin
doaj   +1 more source

Decomposing the complete r-graph

Journal of Combinatorial Theory, Series A, 2018
Let $f_r(n)$ be the minimum number of complete $r$-partite $r$-graphs needed to partition the edge set of the complete $r$-uniform hypergraph on $n$ vertices. Graham and Pollak showed that $f_2(n) = n-1$. An easy construction shows that $f_r(n)\le (1-o(1))\binom{n}{\lfloor r/2\rfloor}$ and it has been unknown if this upper bound is asymptotically sharp.
Imre Leader, Luka Milićević, Ta Sheng Tan   +2 more
openaire   +4 more sources

Decompositions of Complete Multipartite Graphs into Complete Graphs

, 2011
Let $k\geq\ell\geq1$ and $n\geq 1$ be integers. Let $G(k,n)$ be the complete $k$-partite graph with $n$ vertices in each colour class. An $\ell$-decomposition of $G(k,n)$ is a set $X$ of copies of $K_k$ in $G(k,n)$ such that each copy of $K_\ell$ in $G(k,n)$ is a subgraph of exactly one copy of $K_k$ in $X$. This paper asks: when does $G(k,n)$ have an $
Fabila-Monroy, Ruy, Wood, David R.
openaire   +2 more sources

GCD-graphs and NEPS of complete graphs

Ars Mathematica Contemporanea, 2012
A gcd-graph is a Cayley graph over a finite abelian group defined by greatest common divisors. Such graphs are known to have integral spectrum. A non-complete extended p-sum, or NEPS in short, is well-known general graph product. We show that the class of gcd-graphs and the class of NEPS of complete graphs coincide.
Klotz, Walter, Sander, Torsten
openaire   +3 more sources

Statistical Properties of SIS Processes with Heterogeneous Nodal Recovery Rates in Networks

Applied Sciences
The modeling and analysis of epidemic processes in networks have attracted much attention over the past few decades. A major underlying assumption is that the recovery process and infection process are homogeneous, allowing the associated theoretical ...
Dongchao Guo, Libo Jiao, Wendi Feng
doaj   +1 more source