The spectrum of a graph is closely related to many parameters. In particular, the spectral gap regular which difference between its valency and second eigenvalue, widely seen an algebraic measure connectivity plays key role in theory expander graphs. this paper, we extend previous work done for graphs bipartite present linear programming method obtaining upper bound on order uniform hypergraph ...

Epilepsy is a disease marked by hypersynchronous bursts of neuronal activity; therefore, identifying the network characteristics of the epileptic brain is important. Juvenile myoclonic epilepsy (JME) represents a common, idiopathic generalized epileptic syndrome, characterized by spike-and-wave discharge (SWD) electroencephalographic (EEG) waveforms. We compare herein the network properties of ...

Consider a genetic locus carrying a strongly beneficial allele which has recently fixed in a large population. As strongly beneficial alleles fix quickly, sequence diversity at partially linked neutral loci is reduced. This phenomenon is known as a selective sweep. The fixation of the beneficial allele not only affects sequence diversity at single neutral loci but also the joint allele distribu...

Let $A$ be a nontrivial abelian group. A connected simple graph $G = (V, E)$ is $A$-\textbf{antimagic} if there exists an edge labeling $f: E(G) \to \setminus \{0\}$ such that the induced vertex $f^+: V(G) A$, defined by $f^+(v) \Sigma$ $\{f(u,v): (u, v) \in \}$, one-to-one map. In this paper, we analyze group-antimagic property for Cartesian products, hexagonal nets and theta graphs.

Recently we investigated in [SIAM J. Optim., 19 (2008), pp. 572–591] hierarchies of semidefinite approximations for the chromatic number χ(G) of a graph G. In particular, we introduced two hierarchies of lower bounds: the “ψ”-hierarchy converging to the fractional chromatic number and the “Ψ”-hierarchy converging to the chromatic number of a graph. In both hierarchies the first order bounds are...

A {\em theta} is a graph made of three internally vertex-disjoint chordless paths $P_1 = \dots b$, $P_2 $P_3 b$ length at least~2 and such that no edges exist between the except incident to $a$ $b$. pyramid} b_1$, b_2$, b_3$ least~1, two which have least 2, $a$, $b_1b_2b_3$ triangle those to~$a$. An \emph{even hole} cycle even length. For non-negative integers $i\leq j\leq k$, let $S_{i,j,k}$ b...

In this paper, two new classes of matrices - Drazin theta matrix and are introduced for a square index \begin{document}$ m $\end{document}. Whenever the is equal to one, we get special case called Group respectively. Several characterizations these matrices, integral representations, representation in lim...

A graph G = (V, E) is called (k, k′)-total weight choosable if the following holds: For any total list assignment L which assigns to each vertex x a set L(x) of k real numbers, and assigns to each edge e a set L(e) of k′ real numbers, there is a mapping f : V ∪ E → R such that f(y) ∈ L(y) for any y ∈ V ∪ E and for any two adjacent vertices x, x′, ∑ e∈E(x) f(e)+f(x) 6= ∑ e∈E(x′) f(e)+f(x ′). We ...