
Unlike an ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a non-membership degree, is a more flexible way to capture uncertainty. In this paper, we have classified the states of intuitionistic Markov chain (IMC) [1] and analyzed the long-run behavior of the system.
A grid is a large-scale geographically distributed hardware and software infrastructure composed of heterogeneous networked resources owned and shared by multiple administrative organizations which are coordinated to provide transparent, dependable, pervasive and consistent computing support to a wide range of applications. One of the major problems in graph theory is to find the oriented diameter of a graph
By a
In this paper, an
Given an undirected 2-edge connected graph, finding a minimum 2-edge connected spanning subgraph is NP-hard. We solve the problem for Butterfly network, Benes network, Honeycomb network and Sierpiński gasket graph.
The Terminal Wiener index
Let
A proper vertex coloring (no two adjacent vertices have the same color) of a graph
Eigenvalues of a graph are the eigenvalues of its adjacency matrix. The multiset of eigenvalues is called the
Given a connected
Structures realized by arrangements of regular hexagons in the plane are of interest in the chemistry of benzenoid hydrocarbons, where perfect matchings correspond to Kekulé structures which feature in the calculation of molecular energies associated with benzenoid hydrocarbon molecules. Mathematically, assembling in predictable patterns is equivalent to packing in graphs. An
ll graphs considered in our study are simple, finite and undirected. A graph is equitable total domination edge addition critical (stable) if the addition of any arbitrary edge changes (does not change) the equitable total domination number. In this paper, we introduce the following new parameters: equitable independent dom- ination number, equitable total domination number and equitable connected domination number and study their stability upon edge addition, on special families of graphs namely cycles, paths and com- plete bipartite graphs. Also the relation among the above parameters is established.
The
A linear layout, or simply a layout, of an undirected graph
A colored layout of a
Let
The labeling
Graph embedding is an important technique used in the study of computational capabilities of processor interconnection networks and task distribution. In this paper, we present an algorithm for embedding the Hypercubes into Banana Trees and Extended Banana Trees and prove its correctness using the Congestion lemma and Partition lemma.
A kernel in a directed graph
Given a graph
Graph embedding problems have gained importance in the field of interconnection networks for parallel computer architectures. In this paper, we prove that grid and cylinder are the subgraphs of certain circulant networks. Further, we present an algorithm to embed tori into certain circulant networks with dilation
Broadcasting is a fundamental information dissemination problem in a connected graph, in which one vertex called the originator disseminates one or more messages to all other vertices in the graph.
Let
The concept of fuzzy local
In this paper, we have calculated the combinatorial counting relations varying over the
A kernel in a directed graph
A double shell is defined to be two edge-disjoint shells with a common apex. In this paper, we prove that double shells (where the shell orders are
A book consists of a line in the 3-dimensional space, called the spine, and a number of pages, each a half-plane with the spine as boundary. A book embedding
In 2004, Blinco et al [1] introduced
In [1] they have also proved a significant result on graph decomposition that if a graph
Motivated by the result of Blinco et al [1], in this paper, we prove that the well-known almost-bipartite graph, the grid with an additional edge,
A set
In this paper we introduce right angle path and layer of an array. We construct Kolakoski array and study some combinatorial proper-ties of Kolakoski array. Also we obtain recurrence relation for layers and special elements.
An
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