{"title":"General Zagreb index of some cactus chains","authors":"Nilanjan De","doi":"10.30538/PSRP-ODAM2019.0008","DOIUrl":"https://doi.org/10.30538/PSRP-ODAM2019.0008","url":null,"abstract":"Abstract: The mathematical chemistry deals with applications of graph theory to study the physicochemical properties of molecules theoretically. A chemical graph is a simple graph where hydrogen depleted atoms are vertices and covalent bonds between them represent the edges. A topological index of a graph is a numeric quantity obtained from the graph mathematically. A cactus graph is a connected graph in which no edges lie in more than one cycle. In this study, we derive exact expressions of general Zagreb index of some cactus chains.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115800236","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":"Minimum degree polynomial of graphs obtained by some graph operators","authors":"B. Basavanagoud, Praveen Jakkannavar","doi":"10.30538/PSRP-ODAM2019.0011","DOIUrl":"https://doi.org/10.30538/PSRP-ODAM2019.0011","url":null,"abstract":"Abstract: The minimum degree matrix MD(G) of a graph G of order n is an n× n symmetric matrix whose (i, j)th entry is min{di, dj} whenever i 6= j, and zero otherwise, where di and dj are the degrees of the ith and jth vertices of G, respectively. In the present work, we obtain the minimum degree polynomial of the graphs obtained by some graph operators (generalized xyz-point-line transformation graphs).","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"230 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120959145","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":"The outer-connected vertex edge domination number in Lexicographic product graphs","authors":"O. Oyewumi, A. Akwu, Obakpo Johnson Ben","doi":"10.30538/PSRP-ODAM2019.0012","DOIUrl":"https://doi.org/10.30538/PSRP-ODAM2019.0012","url":null,"abstract":"An outer-connected vertex edge dominating set (OCVEDS) for an arbitrary graph G is a set D ⊂ V(G) such that D is a vertex edge dominating set and the graph G D is connected. The outer-connected vertex edge domination number of G is the cardinality of a minimum OCVEDS of G, denoted by γoc ve(G). In this paper, we give the outer-connected vertex edge dominating set in lexicographic product of graphs.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129526557","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}
Abdualrazaq Sanbo, E. Elsayed, Tvtc B.P. Jeddah Saudi Arabia Electronics
{"title":"Some properties of the solutions of the difference equation (x_{n+1}=a x_{n}+dfrac{b x_{n} x_{n-4}}{c x_{n-3}+dx_{n-4}})","authors":"Abdualrazaq Sanbo, E. Elsayed, Tvtc B.P. Jeddah Saudi Arabia Electronics","doi":"10.30538/PSRP-ODAM2019.0014","DOIUrl":"https://doi.org/10.30538/PSRP-ODAM2019.0014","url":null,"abstract":"","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"162 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122763153","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":"Bounds on the covering radius of some classes of codes over R","authors":"P. C. Pandian","doi":"10.30538/PSRP-ODAM2019.0007","DOIUrl":"https://doi.org/10.30538/PSRP-ODAM2019.0007","url":null,"abstract":"In this paper, the covering radius of codes over R = Z2R∗, where R∗ = Z2 + vZ2, v2 = v with different weight are discussed. The block repetition codes over R is defined and the covering radius for block repetition codes, simplex code of α-type and β-type in R are obtained.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133075038","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":"Analysis of the qualitative behaviour of an eighth-order fractional difference equation","authors":"M. Almatrafi, M. M. Alzubaidi","doi":"10.30538/PSRP-ODAM2019.0010","DOIUrl":"https://doi.org/10.30538/PSRP-ODAM2019.0010","url":null,"abstract":"Abstract: The exact solutions of most nonlinear difference equations cannot be obtained theoretically sometimes. Therefore, a massive number of researchers predict the long behaviour of most difference equations by investigating some qualitative behaviours of these equations from the governing equations. In this article, we aim to analyze the asymptotic stability, global stability, periodicity of the solution of an eighth-order difference equation. Moreover, a theoretical solution of a special case equation will be presented in this paper.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129479376","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":"On further results of hex derived networks","authors":"Haidar Ali, Ammara Sajjad","doi":"10.30538/PSRP-ODAM2019.0009","DOIUrl":"https://doi.org/10.30538/PSRP-ODAM2019.0009","url":null,"abstract":"Topological indices are real numbers associated with molecular graphs of compounds that help to guess properties of compounds. Hex-Derived networks has an assortment of valuable applications in drug store, hardware, and systems administration. Imran et al. [1] computed the general Randić, first Zagreb, ABC, GA, ABC4, and GA5 indices for these hex-derived networks. In this article, we extend the work of [1] and compute some new topological indices of these networks.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114069345","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":"The number of extended irreducible binary Goppa codes of degree (2ℓ)m and length 2n+1","authors":"A. Musukwa, Mzuzu Malawi.. Bag","doi":"10.30538/PSRP-ODAM2019.0006","DOIUrl":"https://doi.org/10.30538/PSRP-ODAM2019.0006","url":null,"abstract":"","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116909861","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}
M. Matejic, E. Milovanovic, P. Milošević, I. Milovanovic
{"title":"A note on the Kirchhoff index of graphs","authors":"M. Matejic, E. Milovanovic, P. Milošević, I. Milovanovic","doi":"10.30538/psrp-odam2019.0017","DOIUrl":"https://doi.org/10.30538/psrp-odam2019.0017","url":null,"abstract":"Let G be a simple connected graph with n vertices, m edges, and a sequence of vertex degrees ∆ = d1 ≥ d2 ≥ · · · ≥ dn = δ > 0. Denote by μ1 ≥ μ2 ≥ · · · ≥ μn−1 > μn = 0 the Laplacian eigenvalues of G. The Kirchhoff index of G is defined as K f (G) = n ∑n−1 i=1 1 μi . A couple of new lower bounds for K f (G) that depend on n, m, ∆ and some other graph invariants are obtained.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134143713","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}
G. Lau, Sin-Min Lee, W. Shiu, North First Avenue Upland Ca Usa
{"title":"On edge-prime cubic graphs with small components","authors":"G. Lau, Sin-Min Lee, W. Shiu, North First Avenue Upland Ca Usa","doi":"10.30538/PSRP-ODAM2019.0015","DOIUrl":"https://doi.org/10.30538/PSRP-ODAM2019.0015","url":null,"abstract":"Gee-Choon Lau1,∗, Sin-Min Lee2 and Wai Chee Shiu3,4 1 Faculty of Computer & Mathematical Sciences, Universiti Teknologi MARA (Segamat Campus), 85000 Johor, Malaysia. 2 1304, North First Avenue, Upland, CA 91786 USA.; sinminlee@gmail.com 3 Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong.; shiu1958@gmail.com 4 College of Global Talents, Beijing Institute of Technology, Zhuhai, China. * Correspondence: geeclau@yahoo.com","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"101 8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120972815","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}