{"title":"THE DISTANCE RELATED SPECTRA OF SOME SUBDIVISION RELATED GRAPHS","authors":"Indulal Gopalapillai, Deena C. Scaria","doi":"10.37418/jcsam.3.1.4","DOIUrl":"https://doi.org/10.37418/jcsam.3.1.4","url":null,"abstract":"Let $G$ be a connected graph with a distance matrix $D$. The distance eigenvalues of $G$ are the eigenvalues of $D$, and the distance energy $E_D(G)$ is the sum of its absolute values. The transmission $Tr(v)$ of a vertex $v$ is the sum of the distances from $v$ to all other vertices in $G$. The transmission matrix $Tr(G)$ of $G$ is a diagonal matrix with diagonal entries equal to the transmissions of vertices. The matrices $D^L(G)= Tr(G)-D(G)$ and $D^Q(G)=Tr(G)+D(G)$ are, respectively, the Distance Laplacian and the Distance Signless Laplacian matrices of $G$. The eigenvalues of $D^L(G)$ ( $D^Q(G)$) constitute the Distance Laplacian spectrum ( Distance Signless Laplacian spectrum ). The subdivision graph $S(G)$ of $G$ is obtained by inserting a new vertex into every edge of $G$. We describe here the Distance Spectrum, Distance Laplacian spectrum and Distance Signless Laplacian spectrum of some types of subdivision related graphs of a regular graph in the terms of its adjacency spectrum. We also derive analytic expressions for the distance energy of $bar{S}(C_p)$, partial complement of the subdivision of a cycle $C_p$ and that of $overline {Sleft( {C_p }right)}$, complement of the even cycle $C_{2p}$.","PeriodicalId":361024,"journal":{"name":"Journal of Computer Science and Applied Mathematics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114593556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"L-MMH: AN IMPROVED AND NOVEL MODEL FOR GROWTH","authors":"Deniz Ünal","doi":"10.37418/JCSAM.3.1.3","DOIUrl":"https://doi.org/10.37418/JCSAM.3.1.3","url":null,"abstract":"Proposing a function for modeling growth is an important development for the curve fitting of data. This study gives a derivation for a new mathematical equation for growth and reports some significant features of this model.","PeriodicalId":361024,"journal":{"name":"Journal of Computer Science and Applied Mathematics","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130870350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"ASYMPTOTIC PROPERTIES IN THE PROBIT-ZERO-INFLATED BINOMIAL REGRESSION MODEL","authors":"A. Diop, Demba Ba, Fatimata Lo","doi":"10.37418/jcsam.3.2.3","DOIUrl":"https://doi.org/10.37418/jcsam.3.2.3","url":null,"abstract":"Zero-inflated regression models have had wide application recently and have provenuseful in modeling data with many zeros. Zero-inflated Binomial (ZIB) regression model is an extension of the ordinary binomial distribution that takes into account the excess of zeros. In comparing the probit model to the logistic model, many authors believe that there is little theoretical justification in choosing one formulation over the other in most circumstances involving binary responses. The logit model is considered to be computationally simpler but it is based on a more restrictive assumption of error independence, although many other generalizations have dealt with that assumption as well. By contrast, the probit model assumes that random errors have a multivariate normal distribution. This assumption makes the probit model attractive because the normal distribution provides a good approximation to many other distributions. In this paper, we develop a maximum likelihood estimation procedure for the parameters of a zero-inflated Binomial regression model with probit link function for both component of the model. We establish the existency, consistency and asymptotic normality of the proposed estimator.","PeriodicalId":361024,"journal":{"name":"Journal of Computer Science and Applied Mathematics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122163376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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