LEADER 03885nam 22006975 450 001 9910299782003321 005 20251116133921.0 010 $a3-662-45843-8 024 7 $a10.1007/978-3-662-45843-3 035 $a(CKB)3710000000337849 035 $a(EBL)1968602 035 $a(OCoLC)900193749 035 $a(SSID)ssj0001424491 035 $a(PQKBManifestationID)11784568 035 $a(PQKBTitleCode)TC0001424491 035 $a(PQKBWorkID)11362918 035 $a(PQKB)11701493 035 $a(DE-He213)978-3-662-45843-3 035 $a(MiAaPQ)EBC1968602 035 $a(PPN)183518209 035 $a(EXLCZ)993710000000337849 100 $a20150112d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe Harary index of a graph /$fby Kexiang Xu, Kinkar Ch. Das, Nenad Trinajsti? 205 $a1st ed. 2015. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2015. 215 $a1 online resource (87 p.) 225 1 $aSpringerBriefs in Mathematical Methods,$x2365-0826 300 $aDescription based upon print version of record. 311 08$a3-662-45842-X 320 $aIncludes bibliographical references at the end of each chapters. 327 $aIntroduction -- Extremal Graphs with Respect to Harary Index -- Relation Between the Harary Index and Related Topological Indices -- Some Properties and Applications of Harary Index -- The Variants of Harary Index -- Open Problems. 330 $aThis is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems. This book is dedicated to Professor Frank Harary (1921?2005), the grandmaster of graph theory and its applications. It has be written by experts in the field of graph theory and its applications. For a connected graph G, as an important distance-based topological index, the Harary index H(G) is defined as the sum of the reciprocals of the distance between any two unordered vertices of the graph G. In this book, the authors report on the newest results on the Harary index of a graph. These results mainly concern external graphs with respect to the Harary index; the relations to other topological indices; its properties and applications to pure graph theory and chemical graph theory; and two significant variants, i.e., additively and multiplicatively weighted Harary indices. In the last chapter, we present a number of open problems related to the Harary index. As such, the book will not only be of interest to graph researchers, but to mathematical chemists as well.  . 410 0$aSpringerBriefs in Mathematical Methods,$x2365-0826 606 $aGraph theory 606 $aCombinatorial analysis 606 $aChemometrics 606 $aGraph Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M29020 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 606 $aMath. Applications in Chemistry$3https://scigraph.springernature.com/ontologies/product-market-codes/C17004 615 0$aGraph theory. 615 0$aCombinatorial analysis. 615 0$aChemometrics. 615 14$aGraph Theory. 615 24$aCombinatorics. 615 24$aMath. Applications in Chemistry. 676 $a511.5 700 $aXu$b Kexiang$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755700 702 $aDas$b Kinkar Ch.$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aTrinajsti?$b Nenad$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299782003321 996 $aThe Harary Index of a Graph$92521520 997 $aUNINA