LEADER 03112nam 22005895 450 001 9910508482303321 005 20251113203421.0 010 $a3-030-88410-4 024 7 $a10.1007/978-3-030-88410-9 035 $a(CKB)5470000001298900 035 $a(MiAaPQ)EBC6796785 035 $a(Au-PeEL)EBL6796785 035 $a(OCoLC)1282008798 035 $a(PPN)258303476 035 $a(DE-He213)978-3-030-88410-9 035 $a(EXLCZ)995470000001298900 100 $a20211031d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGraphs from Rings /$fby David F. Anderson, T. Asir, Ayman Badawi, T. Tamizh Chelvam 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (548 pages) $cillustrations 225 1 $aMathematics and Statistics Series 311 08$a3-030-88409-0 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Distances in zero-divisor graphs -- Properties of zero-divisor graphs -- Genus of zero-divisor graphs -- Zero-divisor graph generalizations -- Total graphs of commutative rings -- Graphs from total graphs -- Generalized total graphs -- Other graphs associated with rings -- Bibliography -- Index. 330 $aThis book gives an overview of research on graphs associated with commutative rings. The study of the connections between algebraic structures and certain graphs, especially finite groups and their Cayley graphs, is a classical subject which has attracted a lot of interest. More recently, attention has focused on graphs constructed from commutative rings, a field of study which has generated an extensive amount of research over the last three decades. The aim of this text is to consolidate this large body of work into a single volume, with the intention of encouraging interdisciplinary research between algebraists and graph theorists, using the tools of one subject to solve the problems of the other. The topics covered include the graphical and topological properties of zero-divisor graphs, total graphs and their transformations, and other graphs associated with rings. The book will be of interest to researchers in commutative algebra and graph theory and anyone interested in learning about the connections between these two subjects. 410 0$aMathematics and Statistics Series 606 $aCommutative algebra 606 $aCommutative rings 606 $aGraph theory 606 $aCommutative Rings and Algebras 606 $aGraph Theory 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 0$aGraph theory. 615 14$aCommutative Rings and Algebras. 615 24$aGraph Theory. 676 $a511.5 676 $a511.5 700 $aAnderson$b David F.$f1948-$01251884 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910508482303321 996 $aGraphs from rings$92901855 997 $aUNINA