University of KashanIranian Journal of Mathematical Chemistry2228-648913420221230On the General Eccentric Distance Sum of Graphs and Trees23925211287910.22052/ijmc.2022.246189.1617ENYetneberk KumaFeyissaDepartment of Applied Mathematics, School of Applied Natural Science, Adama Science and Technology University, Adama, Ethiopia0000-0003-0389-8605MuhammadImranDepartment of Mathematical Sciences, Colleges of Science, United Arab Emirates University, Al Ain, United Arab EmiratesTomasVetrikDepartment of Mathematics and Applied Mathematics, University of the Free State, Bloemfontein, South Africa0000000203877276NateaHundeDepartment of Applied Mathematics, School of Applied Natural Science, Adama Science and Technology University, Adama, EthiopiaJournal Article20220321We obtain some sharp bounds on the general eccentric distance sum for general graphs, bipartite graphs and trees with given order and diameter 3, graphs with given order and domination number 2, and for the join of two graphs with given order and number of vertices having maximum possible degree. Extremal graphs are presented for all the bounds.https://ijmc.kashanu.ac.ir/article_112879_5c9c78fc8f09b0019075aba7cdffb474.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648913420221230On Selected Properties of the Gibbs Function Topological Manifold25328011288110.22052/ijmc.2022.246694.1642ENJanTurulskiThird Age University, 16035 Czarna Wies Koscielna, Poland, and
Chemistry Institute, University at Bialystok, 15443, Bialystok, Poland0000-0002-6798-8143Journal Article20220730Quantitatively, the equilibrium in classical thermodynamics in the C-component isobaric-isothermal system is determined by the minimum value of the Gibbs function. The topological manifold of this function is a 2-D dimensional, smooth piece, geometric creation. These pieces represent individual states of single-phase systems. Successive pieces of the manifold are glued along the line of phase transitions to form the manifold of the whole, en bloc, C-component system. Gluing smooth pieces together must guarantee the continuity of the glued whole. The study found the dependence of the number of ways of gluing single-phase pieces on the number of components of the system. It has also been shown that the distribution of components in individual phases of the system is represented by a planar graph with 4 faces, called a normal graph.<br />Studies of the topological properties of the manifold fragments representing single-phase equilibrium states indicate that the value of the Gibbs potential in these states is encoded in the geometry of the topological manifold. In concrete terms, this value is equal to the length of the minimum path lying on the surface of the manifold, connecting the various degrees of freedom of the system (the vertices of the graph). In complex systems, with very large C, the number of paths connecting the degrees of freedom is monstrously large. Preliminary calculations show that in such systems the number of paths with a minimum length or not much different from it may be greater than one.https://ijmc.kashanu.ac.ir/article_112881_ccf91230b0ce05a8b215eb9de4f87501.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648913420221230Extremal Trees for Sombor Index with Given Degree Sequence28129011290910.22052/ijmc.2022.248570.1676ENFatemeMovahediDepartment of Mathematics, Faculty of Sciences, Golestan University, Gorgan, IranJournal Article20221118Let G=(V, E) be a simple graph with vertex set V and edge set E. The Sombor index of the graph G is a degree-based topological index, defined as SO(G)= ∑<sub>uv∈E </sub>√(d(u)<sup>2</sup>+d(v)<sup>2</sup>), in which d(x) is the degree of the vertex x∈V for x=u, v. In this paper, we characterize the extremal trees with given degree sequence that minimizes and maximizes the Sombor index.https://ijmc.kashanu.ac.ir/article_112909_71e766ebb722b78d0a27125112460352.pdf