Fundamenta Informaticae - Volume 191, issue 1

Authors: Dangalchev, Chavdar

Article Type: Research Article

Abstract: The study of networks characteristics is an important subject in different fields, like math, chemistry, transportation, social network analysis etc. The residual closeness is one of the most sensitive measure of graphs’ vulnerability. In this article we calculate the link residual closeness of Harary graphs.

Keywords: Closeness, Residual Closeness, Harary Graphs

DOI: 10.3233/FI-242170

Citation: Fundamenta Informaticae, vol. 191, no. 1, pp. 1-15, 2024

Authors: Jiménez González, Jesús Arturo

Article Type: Research Article

Abstract: An integral quadratic form q : ℤn → ℤ is usually identified with a bilinear form 𝕓 ∨ q : ℤ n × ℤ n → ℤ satisfying q ( x ) = 𝕓 ∨ q ( x , x ) for any vector x in ℤn , and such that its Gram matrix with respect to the canonical basis of ℤn is upper triangular. Two integral quadratic forms are called strongly (resp. weakly) Gram congruent if …their corresponding upper triangular bilinear forms (resp. their symmetrizations) are equivalent. If q is unitary, such upper triangular bilinear form is unimodular, and one considers the associated Coxeter transformation and its characteristic polynomial, the so-called Coxeter polynomial of q with this identification. Two strongly Gram congruent quadratic unit forms are weakly Gram congruent and have the same Coxeter polynomial. Here we show that the converse of this statement holds for the connected non-negative case of Dynkin type 𝔸r (r ≥ 1) and arbitrary corank, and use this characterization to complete a combinatorial classification of such quadratic forms started in [Fundamenta Informaticae 184 (1):49–82, 2021] and [Fundamenta Informaticae 185 (3):221–246, 2022]. Show more

Keywords: Integral quadratic form, Gram congruence, Dynkin type, Coxeter polynomial, edge-bipartite graph, quiver, incidence matrix, signed line graph, 2020 MSC: 15A63, 15A21, 15B36, 05C22, 05C50, 05C76, 05B20

DOI: 10.3233/FI-242171

Citation: Fundamenta Informaticae, vol. 191, no. 1, pp. 17-66, 2024

Authors: Zhou, Sizhong | Wu, Jiancheng

Article Type: Research Article

Abstract: Let 𝒜 be a set of connected graphs. Then a spanning subgraph A of G is called an 𝒜-factor if each component of A is isomorphic to some member of 𝒜. Especially, when every graph in 𝒜 is a path, A is a path factor. For a positive integer d ≥ 2, we write 𝒫≥d = {𝒫i |i ≥ d }. Then a 𝒫≥d -factor means a path factor in which every component admits at least d vertices. A graph G is called a (𝒫≥d ,m )-factor …deleted graph if G – E ′ admits a 𝒫≥d -factor for any E ′ ⊆ E (G ) with |E ′| = m . A graph G is called a (𝒫≥d , k)-factor critical graph if G – Q has a 𝒫≥d -factor for any Q ⊆ V (G ) with |Q | = k . In this paper, we present two degree conditions for graphs to be (𝒫≥3 ,m )-factor deleted graphs and (𝒫≥3 , k )-factor critical graphs. Furthermore, we show that the two results are best possible in some sense. Show more

Keywords: graph, degree condition, 𝒫≥3-factor, (𝒫≥3,m)-factor deleted graph, (𝒫≥3,k)-factor critical graph, (2020) Mathematics Subject Classification: 05C70, 05C38

DOI: 10.3233/FI-242172

Citation: Fundamenta Informaticae, vol. 191, no. 1, pp. 67-77, 2024