Introduction/purpose: The Euler-Sombor index (EU) is a new vertexdegree-based graph invariant, obtained by geometric consideration. It is closely related to the Sombor index (SO). The actual form of ...this relation is established. Methods: Combinatorial graph theory is applied. Results: The inequalities between EU and SO are established. Conclusion: The paper contributes to the theory of Sombor-index-like graph invariants.
Introduction/purpose: The entire topological indices (T Ient) are a class of graph invariants depending on the degrees of vertices and edges. Some general properties of these invariants are ...established. Methods: Combinatorial graph theory is applied. Results: A new general expression for T Ient is obtained. For triangle-free and quadrangle-free graphs, this expression can be significantly simplified. Conclusion: The paper contributes to the theory of vertex and edge degree-based graph invariants.
Introduction/purpose: The temperature of a vertex of a graph of the order n is defined as d/(n-d), where d is the vertex degree. The temperature variant of the Sombor index is investigated and ...several of its properties established. Methods: Combinatorial graph theory is applied. Results: Extremal values and bounds for the temperature Sombor index are obtained. Conclusion: The paper contributes to the theory of Sombor-index-like graph invariants.
Introduction/purpose: Vertex-degree-based (VDB) graph matrices form a special class of matrices, corresponding to the currently much investigated vertex-degree-based (VDB) graph invariants. Some ...spectral properties of these matrices are investigated. Results: Generally valid sharp lower and upper bounds are established for the spectral radius of any VDB matrix. The equality cases are characterized. Several earlier published results are shown to be special cases of the presently reported bounds. Conclusion: The results of the paper contribute to the general spectral theory of VDB matrices, as well as to the general theory of VDB graph invariants.
Introduction/purpose: In the current literature, several dozens of vertex-degree-based (VDB) graph invariants are being studied. To each such invariant, a matrix can be associated. The VDB energy is ...the energy (= sum of the absolute values of the eigenvalues) of the respective VDB matrix. The paper examines some general properties of the VDB energy of bipartite graphs. Results: Estimates (lower and upper bounds) are established for the VDB energy of bipartite graphs in which there are no cycles of size divisible by 4, in terms of ordinary graph energy. Conclusion: The results of the paper contribute to the spectral theory of VDB matrices, especially to the general theory of VDB energy.
Introduction/purpose: The Sombor matrix is a vertex-degree-based matrix associated with the Sombor index. The paper is concerned with the spectral properties of the Sombor matrix. Results: Equalities ...and inequalities for the eigenvalues of the Sombor matrix are obtained, from which two fundamental bounds for the Sombor energy (= energy of the Sombor matrix) are established. These bounds depend on the Sombor index and on the "forgotten" topological index. Conclusion: The results of the paper contribute to the spectral theory of the Sombor matrix, as well as to the general spectral theory of matrices associated with vertex-degree-based graph invariants.
This book is about graph energy. The authors have included many of the important results on graph energy, such as the complete solution to the conjecture on maximal energy of unicyclic graphs, the ...Wagner-Heubergers result on the energy of trees, the energy of random graphs or the approach to energy using singular values. It contains an extensive coverage of recent results and a gradual development of topics and the inclusion of complete proofs from most of the important recent results in the area. The latter fact makes it a valuable reference for researchers looking to get into the field of graph energy, further stimulating it with occasional inclusion of open problems. The book provides a comprehensive survey of all results and common proof methods obtained in this field with an extensive reference section. The book is aimed mainly towards mathematicians, both researchers and doctoral students, with interest in the field of mathematical chemistry.
Beyond the Zagreb indices Gutman, Ivan; Milovanović, Emina; Milovanović, Igor
AKCE International Journal of Graphs and Combinatorics,
01/2020, Letnik:
17, Številka:
1
Journal Article
Recenzirano
Odprti dostop
The two Zagreb indices M1=∑vd(v)2 and M2=∑uvd(u)d(v) are vertex-degree-based graph invariants that have been introduced in the 1970s and extensively studied ever since. In the last few years, a ...variety of modifications of M1 and M2 were put forward. The present survey of these modified Zagreb indices outlines their main mathematical properties, and provides an exhaustive bibliography.
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