https://scidar.kg.ac.rs/handle/123456789/8214 Sun, 10 May 2026 07:09:56 GMT 2026-05-10T07:09:56Z http://https://scidar.kg.ac.rs:80/retrieve/2068baf0-71c7-41b7-a42d-0981de30e08f/b49a481c-06a6-432f-88fb-a9322c278510.png https://scidar.kg.ac.rs/handle/123456789/8214 https://scidar.kg.ac.rs/handle/123456789/23123 Title: On the Hamming Spectrum and Hamming Energy of Graphs Authors: Borovićanin, Bojana; Stojanović, Nenad; Vučićević, Nemanja Abstract: In this paper, we study the spectrum of the Hamming matrix H(G) of a simple graph G. The Hamming matrix, recently introduced in terms of the Hamming distances between binary strings derived from the incidence matrix, offers an alternative and insightful perspective on spectral and chemical graph theory. We derive upper and lower bounds for the largest and smallest eigenvalues of the Hamming matrix of paths, respectively, as well as closed-form expressions for the Hamming spectrum and Hamming energy of regular graphs (including cycles as a special case), their complements, and their line graphs, with respect to the classical adjacency spectrum. Furthermore, we provide a factorization that relates the characteristic polynomial of the Hamming matrix of a regular graph to that of its complement and its line graph. These results shed new light on how Hamming-based invariants interact with classical spectral quantities. Thu, 01 Jan 2026 00:00:00 GMT https://scidar.kg.ac.rs/handle/123456789/23123 2026-01-01T00:00:00Z https://scidar.kg.ac.rs/handle/123456789/23122 Title: On the geometric-arithmetic index Authors: Milivojević-Danas, Milica; Pavlović, Ljiljana Editors: Tomović, Tatjana Mon, 01 Jan 2018 00:00:00 GMT https://scidar.kg.ac.rs/handle/123456789/23122 2018-01-01T00:00:00Z https://scidar.kg.ac.rs/handle/123456789/23121 Title: METRIC DIMENSION OF COMPLETE SPLIT GRAPHS Authors: Kratica, Jozef; Milivojević-Danas, Milica Abstract: In this paper, the problem of determining the metric dimension for special class of graphs, named complete split graphs 𝐾^∗_{𝑘,𝑛−𝑘} is considered. It is stated and proved formula for the metric dimension of this graphs: for 𝑛 − 𝑘 ≥ 2 and 𝑘 ≥ 2, as well as for 𝑘 = 1 and 𝑛 ≥ 3, metric dimension of 𝐾^∗_{𝑘,𝑛−𝑘} is equal to n −2, otherwise metric dimension of 𝐾^∗_{𝑘,𝑛−𝑘} is equal to 𝑛 − 1. Sat, 01 Jan 2022 00:00:00 GMT https://scidar.kg.ac.rs/handle/123456789/23121 2022-01-01T00:00:00Z https://scidar.kg.ac.rs/handle/123456789/23095 Title: Algorithms for Decision-Making Based on Energies of Probabilistic and Dual Probabilistic Soft Set Authors: Vučićević, Nemanja; Stojanović, Nenad; Sezgin , Aslıhan Abstract: After introducing the concepts of soft sets and graph energy as independent terms from different areas of mathematics, there has been significant application of both concepts. The theory of soft sets has been combined with other theories, such as fuzzy set theory and probability theory. From this combination with probability theory, a structure known as probabilistic soft set has emerged, which has been discussed relatively little in the context of decision-making. In this paper, we propose new decision-making algorithms based on numerical characteristics, which we call energies of probabilistic soft sets and dual probabilistic soft sets. The introduced concept of energy for probabilistic soft sets and dual probabilistic soft sets originated from integrating the idea of graph energy into probabilistic soft sets. The paper also presents a comparison of the obtained results using energy with results obtained by other algorithms. Thu, 01 Jan 2026 00:00:00 GMT https://scidar.kg.ac.rs/handle/123456789/23095 2026-01-01T00:00:00Z