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1.
On edge connectivity of direct products of graphs
Xiang-Lan Cao, Špela Brglez, Simon Špacapan, Elkin Vumar, 2011, izvirni znanstveni članek

Opis: Let ▫$lambda(G)$▫ be the edge connectivity of ▫$G$▫. The direct product of graphs ▫$G$▫ and ▫$H$▫ is the graph with vertex set ▫$V(G times H) = V(G) times V(H)$▫, where two vertices ▫$(u_1,v_1)$▫ and ▫$(u_2,v_2)$▫ are adjacent in ▫$G times H$▫ if ▫$u_1u_2 in E(G)$▫ and ▫$v_1v_2 in E(H)$▫. We prove that ▫$lambda(G times K_n) = min{n(n-1)lambda(G), (n-1)delta(G)}$▫ for every nontrivial graph ▫$G$▫ and ▫$n geqslant 3$▫. We also prove that for almost every pair of graphs ▫$G$▫ and ▫$H$▫ with ▫$n$▫ vertices and edge probability ▫$p$▫, ▫$G times H$▫ is ▫$k$▫-connected, where ▫$k=O((n/log n)^2)$▫.
Ključne besede: mathematics, graph theory, combinatorial problems, connectivity, direct product, graph product, separating set
Objavljeno: 01.06.2012; Ogledov: 1457; Prenosov: 170
URL Povezava na celotno besedilo

2.
Application of Mawhin’s coincidence degree and matrix spectral theory to a delayed system
Yong-Hui Xia, Xiang Gu, Patricia Wong J. Y., Syed Abbas, 2012, izvirni znanstveni članek

Opis: This paper gives an application of Mawhin’s coincidence degree and matrix spectral theory to a predator-prey model with M-predators and N-preys. The method is different from that used in the previous work. Some new sufficient conditions are obtained for the existence and global asymptotic stability of the periodic solution. The existence and stability conditions are given in terms of spectral radius of explicit matrices which are much different from the conditions given by the algebraic inequalities. Finally, an example is given to show the feasibility of our results.
Ključne besede: coincidence degree, Jean Mawhin, predator-prey model, spectral theory
Objavljeno: 12.06.2017; Ogledov: 415; Prenosov: 94
.pdf Celotno besedilo (2,05 MB)

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