Complementary to the fancy big data applications, networking for is an indispensable supporting platform these applications in practice. This emerging research branch has gained extensive attention from both academia and industry recent years. In this new territory, researchers are facing many unprecedented theoretical practical challenges. We therefore motivated solicit latest works area, aiming pave a comprehensive solid starting ground interested readers. first clarify definition of based...

We survey some of the known results on eigenvalues Cayley graphs and their applications, together with related digraphs generalizations graphs.

Given a graph $\Gamma$, subset $C$ of $V(\Gamma)$ is called perfect code in $\Gamma$ if every vertex at distance no more than one to exactly $C$, and total adjacent $C$. In this paper we study codes Cayley graphs, with focus on the following themes: when subgroup given group (total) group; how construct new from known ones using automorphisms underlying group. We prove several results around these questions.

This article focuses on electric load forecasting, which is a challenging task in the energy industry. In this paper, novel kernel-free $$\nu $$ -support vector regression model proposed for forecasting. The produces reduced quadratic surface nonlinear regression. A feature weighting strategy adopted to estimate relevance of features history. To reduce effects outliers history, weight assigned represent relative importance each data point. Some computational experiments are conducted some...

We say that a group is $4$-HAT-stabilizer if it the vertex stabilizer of some connected $4$-valent half-arc-transitive graph. In 2001, Maru\v{s}i\v{c} and Nedela proved every must be concentric group. However, over past two decades, only very small proportion groups have been shown to $4$-HAT-stabilizers. This paper develops theory provides general framework for determining whether $4$-HAT-stabilizer. With this approach, we significantly extend known list As corollary, confirm...

We study a class of Cayley graphs as models for interconnection networks. With focus on efficient communication we prove that any graph in the there exists gossiping protocol which exhibits attractive features, and, moreover, give an algorithm constructing such protocol. In particular, these hold two important subclasses graphs, namely, admitting complete rotation and Frobenius certain type. For obtain minimum gossip time optimal under messages are transmitted along shortest paths each arc...

Given simple graphs and , the neighbourhood corona of denoted is graph obtained by taking one copy copies joining neighbours th vertex to every in . In this paper we determine adjacency spectrum for arbitrary Laplacian signless regular terms corresponding The results on spectra enable us construct new pairs cospectral graphs. As applications spectra, give constructions families expander from known ones using coronae.

Let $R$ be a finite commutative ring. The unitary Cayley graph of $R$, denoted $G_R$, is the with vertex set and edge $\left\{\{a,b\}:a,b\in R, a-b\in R^\times\right\}$, where $R^\times$ units $R$. An $r$-regular Ramanujan if absolute value every eigenvalue it other than $\pm r$ at most $2\sqrt{r-1}$. In this paper we give necessary sufficient condition for $G_R$ to Ramanujan, complement Ramanujan. We also determine energy line compute spectral moments its graph.

Let $\Gamma$ be a graph with vertex set $V(\Gamma)$. A subset $C$ of $V(\Gamma)$ is called perfect code in if an independent and every $V(\Gamma)\setminus C$ adjacent to exactly one $C$. group $G$ there exists Cayley which admits as code. said code-perfect proper subgroup $G$. In this paper we prove that only it has no elements order 4. We also $H$ abelian the Sylow 2-subgroup This reduces problem determining when given case 2-groups. Finally, determine all codes any generalized quaternion group.

Abstract The decycling number ϕ( G ) of a graph is the smallest vertices which can be removed from so that resultant contains no cycles. In this paper, we study numbers random regular graphs. For cubic order n , prove = ⌈ /4 + 1/2⌉ holds asymptotically almost surely. This result executing greedy algorithm for making use randomly chosen Hamilton cycle. general d ‐regular where ≥ 4, )/ bounded below and above surely by certain constants b ( B ), depending solely on are determined solving,...

In this paper, we introduce a decomposition theory for fuzzy cognitive maps (FCM). First, partition the set of vertices an FCM into blocks according to equivalence relation, and by regarding these as construct quotient FCM. Second, each block induces natural sectional original FCM, which inherits topological structure well inference from way, decompose some As result, analysis is reduced are often much smaller in size complexity. Such reduction important analyzing large-scale We also propose...

In this paper, we first propose a general framework for fuzzy causal networks (FCNs). Then, study the dynamics and convergence of such FCNs. We prove that any FCN with constant weight matrix converges to limit cycle or static state, trajectory is not repetitive. also under certain conditions discrete state its in O(n) steps, where n number vertices FCN. This striking contrast exponential running time 2/sup n/, which accepted widely classic

This paper presents a dynamic domination theory for fuzzy causal networks (FCN). There are three major contributions. First, we propose new inference procedure based on dominating sets. Second, introduce the concepts of and minimal sets (DDS MDDS) in an FCN. To reflect changes dominance with time, also concept process (DDP) that has significant implications many real-world problems. We pay special attention to (MDDP) develop rules generating DDP MDDP. Third, investigate extended feedback,...