University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 13 4 2022 12 01 On the General Eccentric Distance Sum of Graphs and Trees 239 252 112879 10.22052/ijmc.2022.246189.1617 EN Yetneberk Kuma Feyissa Department of Applied Mathematics, School of Applied Natural Science, Adama Science and Technology University, Adama, Ethiopia Muhammad Imran Department of Mathematical Sciences, Colleges of Science, United Arab Emirates University, Al Ain, United Arab Emirates Tomas Vetrik Department of Mathematics and Applied Mathematics, University of the Free State, Bloemfontein, South Africa 0000-0002-0387-7276 Natea Hunde Department of Applied Mathematics, School of Applied Natural Science, Adama Science and Technology University, Adama, Ethiopia Journal Article 2022 03 21 We 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.pdf

University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 13 4 2022 12 01 On Selected Properties of the Gibbs Function Topological Manifold 253 280 112881 10.22052/ijmc.2022.246694.1642 EN Jan Turulski Third Age University, 16035 Czarna Wies Koscielna, Poland, and Chemistry Institute, University at Bialystok, 15443, Bialystok, Poland Journal Article 2022 07 30 Quantitatively, 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. 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.pdf

University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 13 4 2022 12 01 Extremal Trees for Sombor Index with Given Degree Sequence 281 290 112909 10.22052/ijmc.2022.248570.1676 EN Fateme Movahedi Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran 0000-0001-7863-7915 Journal Article 2022 11 18 Let 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)= ∑uv∈E √(d(u)2+d(v)2), 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

University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 13 4 2022 12 01 On Color Matrix and Energy of Semigraphs 291 299 113679 10.22052/ijmc.2022.246186.1616 EN Ardhendu Kumar Nandi Department of Mathematics, Basugaon College, P.O. Basugaon, 783372, India Ivan Gutman Faculty of Science, University of Kragujevac, P.O. Box 60, 34000 Kragujevac, Serbia Surajit Kumar Nath Department of Mathematical Sciences, Bodoland University, P.O. Kokrajhar, 783370, India Journal Article 2022 03 20 We introduce the concept of color matrix and color energy of semigraphs. The color energy is the sum of the absolute values of the eigenvalues of the color matrix. Some properties and bounds on color energy of semigraphs are established.

https://ijmc.kashanu.ac.ir/article_113679_f5d58787104e45b02f48afa81d4eb813.pdf

University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 13 4 2022 12 01 Generalized Schultz and Gutman Indices 301 316 113681 10.22052/ijmc.2022.246460.1629 EN Shaikh Ameer Basha Department of Mathematics, Bearys Institute of Technology, Mangaluru-574199, Karnataka, INDIA 0000-0003-1641-4614 Thejur Venkategowda Asha Department of Mathematics, Bangalore University, Janabharathi Campus, Bengaluru-560 056, Karnataka, INDIA Basavaraju Chaluvaraju Department of Mathematics, Bangalore University, Janabharathi Campus, Bengaluru-560 056, Karnataka, INDIA Journal Article 2022 06 04 The degree and distance both are significant concepts in graphs with widespread utilization. The combined study of these concepts has given a new direction to the topological in- dices. In this article, we present the generalized degree distance indices (Generalized First Schultz indices) DD(a;b), and generalized Gutman indices (Second Schultz indices) ZZ(a;b). The computed values of these indices on certain families of graphs along with some bounds and characterizations are obtained. Also, we present the relationship between DD(a;b) and ZZ(a;b). Further, we present the Schultz polynomials along with the statistical analysis of certain graphs.

https://ijmc.kashanu.ac.ir/article_113681_9906b032c292d8e4d9c8294b9ae8f579.pdf