Autor: Zhang, Heping - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: A Maximum Resonant Set of Polyomino Graphs
Autorzy:: Zhang, Heping
Zhou, Xiangqian
Powiązania:: https://bibliotekanauki.pl/articles/31340955.pdf
Data publikacji:: 2016-05-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: polyomino graph
dimer problem
perfect matching
resonant set
forcing number
alternating set
Opis:: A polyomino graph P is a connected finite subgraph of the infinite plane grid such that each finite face is surrounded by a regular square of side length one and each edge belongs to at least one square. A dimer covering of P corresponds to a perfect matching. Different dimer coverings can interact via an alternating cycle (or square) with respect to them. A set of disjoint squares of P is a resonant set if P has a perfect matching M so that each one of those squares is M-alternating. In this paper, we show that if K is a maximum resonant set of P, then P − K has a unique perfect matching. We further prove that the maximum forcing number of a polyomino graph is equal to the cardinality of a maximum resonant set. This confirms a conjecture of Xu et al. [26]. We also show that if K is a maximal alternating set of P, then P − K has a unique perfect matching.
Źródło:: Discussiones Mathematicae Graph Theory; 2016, 36, 2; 323-337
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: A Note on the Permanental Roots of Bipartite Graphs
Autorzy:: Zhang, Heping
Liu, Shunyi
Li, Wei
Powiązania:: https://bibliotekanauki.pl/articles/30147218.pdf
Data publikacji:: 2014-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: permanent
permanental polynomial
permanental roots
Opis:: It is well-known that any graph has all real eigenvalues and a graph is bipartite if and only if its spectrum is symmetric with respect to the origin. We are interested in finding whether the permanental roots of a bipartite graph G have symmetric property as the spectrum of G. In this note, we show that the permanental roots of bipartite graphs are symmetric with respect to the real and imaginary axes. Furthermore, we prove that any graph has no negative real permanental root, and any graph containing at least one edge has complex permanental roots.
Źródło:: Discussiones Mathematicae Graph Theory; 2014, 34, 1; 49-56
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Extremal Matching Energy of Complements of Trees
Autorzy:: Wu, Tingzeng
Yan, Weigen
Zhang, Heping
Powiązania:: https://bibliotekanauki.pl/articles/31340889.pdf
Data publikacji:: 2016-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: matching polynomial
matching energy
Hosoya index
energy
Opis:: Gutman and Wagner proposed the concept of the matching energy which is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph. And they pointed out that the chemical applications of matching energy go back to the 1970s. Let $T$ be a tree with n vertices. In this paper, we characterize the trees whose complements have the maximal, second-maximal and minimal matching energy. Furthermore, we determine the trees with edge-independence number p whose complements have the minimum matching energy for $ p = 1, 2, . . ., \floor{ n/2 } $. When we restrict our consideration to all trees with a perfect matching, we determine the trees whose complements have the second-maximal matching energy.
Źródło:: Discussiones Mathematicae Graph Theory; 2016, 36, 3; 505-521
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: Per-Spectral Characterizations Of Some Bipartite Graphs
Autorzy:: Wu, Tingzeng
Zhang, Heping
Powiązania:: https://bibliotekanauki.pl/articles/31341599.pdf
Data publikacji:: 2017-11-27
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: permanent
permanental polynomial
per-spectrum
cospectral
Opis:: A graph is said to be characterized by its permanental spectrum if there is no other non-isomorphic graph with the same permanental spectrum. In this paper, we investigate when a complete bipartite graph K_p,p with some edges deleted is determined by its permanental spectrum. We first prove that a graph obtained from K_p,p by deleting all edges of a star K_1,l, provided l < p, is determined by its permanental spectrum. Furthermore, we show that all graphs with a perfect matching obtained from K_p,p by removing five or fewer edges are determined by their permanental spectra.
Źródło:: Discussiones Mathematicae Graph Theory; 2017, 37, 4; 935-951
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 5.

Tytuł:: Sharp Upper Bounds on the Clar Number of Fullerene Graphs
Autorzy:: Gao, Yang
Zhang, Heping
Powiązania:: https://bibliotekanauki.pl/articles/31342425.pdf
Data publikacji:: 2018-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: fullerene
Clar number
Clar set
leapfrog transformation
Opis:: The Clar number of a fullerene graph with $n$ vertices is bounded above by $ \floor { n // 6 } − 2 $ and this bound has been improved to $ \floor{ n//6 } − 3 $ when $n$ is congruent to 2 modulo 6. We can construct at least one fullerene graph attaining the upper bounds for every even number of vertices $ n \ge 20 $ except $n = 22 $ and $ n = 30 $.
Źródło:: Discussiones Mathematicae Graph Theory; 2018, 38, 1; 155-163
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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