Equiseparable molecules and molecular graphs

Abstract

By deleting an edge <i>e_i</i> from the molecular graph <i>G</i> of an acyclic molecule, it decomposes into two fragments, with <i>n</i>_l(<i>e_i</i><i><span dir="RTL" style="font-size:12.0pt;font-family:" times="" new="" roman";="" mso-bidi-language:he"="" lang="HE">│</span></i><i>G</i>) and vertices, <i>n</i>_l(<i>e_i</i><i><span dir="RTL" style="font-size:12.0pt;font-family: " times="" new="" roman";mso-bidi-language:he"="" lang="HE">│</span></i><i>G</i>) ≤ <i>n</i>₂(<i>e_i</i><i><span dir="RTL" style="font-size:12.0pt;font-family: " times="" new="" roman";mso-bidi-language:he"="" lang="HE">│</span></i><i>G</i>) <i>i=1,2,..,m. </i>If the edges of the graphs <i>G</i>ʹ and <i>G", </i>representing two isomeric acyclic molecules, can be chosen so that <i>n</i>_l(<i>e_i</i><i><span dir="RTL" style="font-size:12.0pt;font-family: " times="" new="" roman";mso-bidi-language:he"="" lang="HE">│</span></i><i>Gʹ</i>)= <i>n</i>_l(<i>e_i</i><i><span dir="RTL" style="font-size:12.0pt;font-family: " times="" new="" roman";mso-bidi-language:he"="" lang="HE">│</span></i><i>Gʹʹ</i>) holds for all <i>i=1.2 .. ...m</i>,<i> </i>then <i>G</i>ʹ and <i>G" </i>are said to be equiseparable. The respective two isomeric molecules are also said to be equiseparable. The main (known) physicochemical consequences of equiseparability are pointed out. A general method for designing pairs of equiseparable molecular graphs is described, by which large sets of equiseparable species can be constructed.