APAV - Academy of Sciences, Letters, Arts and Technology (E-Journals)
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Forcing vertex square free detour number of a graph
Full text linkLet G be a connected graph and S a square free detour basis of G. A subset T\subseteq S is called a forcing subset for S if S is the unique square free detour basis of S containing T. A forcing subset for S of minimum order is a minimum forcing subset of G. The forcing square free detour number of G is fdn◻fu(G)=minfdn◻fuSu, where the minimum is taken over all square free detour bases S in G. In this paper, we introduce the forcing vertex square free detour sets. The general properties satisfied by these forcing subsets are discussed and the forcing square free detour number for a certain class of standard graphs are determined. We show that the two parameters dn◻fu(G) and fdn◻fu(G) satisfy the relationship 0\le fdn◻fu(G)≤dn◻fu(G). Also, we prove the existence of a graph G with fdn◻fu(G)=α and dn◻fu(G)=β, where 0\le\alpha\le\beta and \beta\geq2 for some vertex u in G
Rainfall Forecast in Different Methods of Trend Equations by Fuzzy Time Series
Full text linkFuzzy time series models have been put forward for Rainfall Prediction from many researchers around the globe. Fuzzy time series methods do not require any assumptions valid for classic time series approaches. The most important disadvantage of fuzzy time series approaches is that it needs subjective decisions, especially in fuzzification stage. This paper proposes a novel improvement of forecasting approach based on using first order fuzzy time series. In contrast to traditional forecasting methods, fuzzy time series can be also applied to problems, in which historical rainfall data of Trichy district. In this study reveals some feature of FTS predicting Rainfall and the results have been compared with other methods
Nano δI-closed Sets in Nano Ideal Topological Spaces
Full text linkThis article investigates the notion of N-δI-closed sets and its properties in ideal nano topological space using the closure operator NclδI(S)={xÎՍ/ Nint(Ncl*(W))∩ S ≠ ∅, for each WÎWN(x)}. We establish NclδI(S) is the intersection of all N-δI-closed supersets of S and NintδI(S) is the union of all N-δI-open subsets of S in this space. Apart from that N-δI-closed sets occurs between the class of Nδ-closed sets and N-closed sets. Moreover, we explore the concepts of N-δI-interior, N-δI-Exterior, N-δI-Border, and N-δI-Frontier and discuss its properties
Some results on range labeling
Full text linkIn this article, We have extended to Range labeling for some trees as for Star trees, Spider trees and Banana tres
Deep Features and Clustering Based Keyframes Selection with Security
Full text linkThe digital world is developing more quickly than ever. Multimedia processing and distribution, however become vulnerable issues due to the enormous quantity and significance of vital information. Therefore, extensive technologies and algorithms are required for the safe transmission of messages, images, and video files. This paper proposes a secure framework by acute integration of video summarization and image encryption. Three parts comprise the proposed cryptosystem framework. The informative frames are first extracted using an efficient and lightweight technique that make use of the color histogram-clustering (RGB-HSV) approach's processing capabilities. Each frame of a video is represented by deep features, which are based on an enhanced pre-trained Inception-v3 network. After that summary is obtain using the K-means optimal clustering algorithm. The representative keyframes then extracted using the clusters highest possible entropy nodes. Experimental validation on two well-known standard datasets demonstrates the proposed methods superiority to numerous state-of-the-art approaches. Finally, the proposed framework performs an efficient image encryption and decryption algorithm by employing a general linear group function GLn (F). The analysis and testing outcomes prove the superiority of the proposed adaptive RSA
Analytical solution of time-fractional N-dimensional Black-Scholes equation using LHPM
Full text linkA famous Black-Scholes differential equation is used for pricing options in financial world which represents financial derivatives more significantly. Option is one of the crucial financial derivatives. Sawangtong P., Trachoo K., Sawangtong W. and Wiwattanapataphee B. obtained analytical solution of Black-Scholes equation with two assets in the Liouville-Caputo time-fractional derivative sense using Laplace homotopy perturbation method (LHPM). The aim of this paper is to derive solution of Liouville-Caputo time-fractional Black-Scholes equation with n assets using LHPM. Numerical results shows that our approach gives very accurate results and our formulas are quite close to the plain vanilla options
sc-graphs
Full text linkAny graph operation of a graph drive only one graph structure. But eccentric graph operation of almost all the graphs drives more than one graph structure, which are interesting and marvelous one. The eccentric graph of G is denoted by ecc(G). Only few families of prime cordial eccentric graphs are investigated. A graph G is separationcordial graph, if it admits separation cordial labeling. In this paper, we investigate some new families of separation cordial eccentric graphs such as ecc(Cn K1), ecc(P(Cn(2))) and ecc(S(m; n))
Relatively Prime Detour Domination Number of Some Switching Graphs
No full textIn this paper, we introduce the concept of relatively prime detour domination number for switching graph. If a set S ⊆ V is a detour set, a dominating set with at least two elements, and has (deg(u), deg(v)) = 1 for each pair of vertices u and v, then it is said to be a relatively prime detour dominating set of a graph G. The relatively prime detour domination number of a graph G is known as γrpdn(G) and represents the lowest cardinality of a relatively prime detour dominating set. First, we explain the concept of a switching graph before producing some conclusions based on the switching graphs of helm, fan, complete, spider, and sunlet graphs that have relatively prime detour domination numbers
On Prime Index of a Graph
Full text linkIn prime labeling, vertices are labeled from 1 to n, with the condition that any two adjacent vertices have relatively prime labels. Coprime labeling maintains the same criterion as prime labeling with adjacent vertices using any set of distinct positive integers. Minimum coprime number prG, is the minimum value k for which G has coprime labeling. There are many graphs that do not possess prime labeling, and hence have coprime labeling. The primary purpose of this work is to change a coprime labeled graph into a prime graph by removing the minimum number of edges. Thus, the prime index ε(G) is the least number of edges to be removed from a coprime graph G to form a prime graph. In this study, the prime index of various graphs is determined. Also, an algorithmic way to determine the prime index of the complete graph is found
Common fixed point theorem for weakly compatible mappings in Sm metric space
Full text linkIn the present paper, at first, we study the structure of the newly Smmetric space, which is a union of S-metric space and multiplicative metric space with new contraction condition. We have proved a common fixed point theorem in Sm metric space by applying the concepts of the weakly compatible mappings, semi-compatible mappings, and reciprocally continuous mappings. This result generalizes and improves many common fixed point theorems in S-metric space and multiplicative metric space . Further, we also provide some examples to support our result