Temat: graph - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Pₘ-saturated bipartite graphs with minimum size
Autorzy:: Dudek, Aneta
Wojda, A.
Tematy:: graph
saturated graph
extremal graph
bipartite graph; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/744479.pdf Link otwiera się w nowym oknie
Opis:: A graph G is said to be H-saturated if G is H-free i.e., (G has no subgraph isomorphic to H) and adding any new edge to G creates a copy of H in G. In 1986 L. Kászonyi and Zs. Tuza considered the following problem: for given m and n find the minimum size sat(n;Pₘ) of Pₘ-saturated graph of order n. They gave the number sat(n;Pₘ) for n big enough. We deal with similar problem for bipartite graphs.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: A Note on Total Graphs
Autorzy:: Forouhandeh, S.F.
Jafari Rad, N.
Vaqari Motlagh, B.H.
Patil, H.P.
Pandiya Raj, R.
Tematy:: total graph
central graph
middle graph
Mycielski graph; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31339326.pdf Link otwiera się w nowym oknie
Opis:: Erratum Identification and corrections of the existing mistakes in the paper On the total graph of Mycielski graphs, central graphs and their covering numbers, Discuss. Math. Graph Theory 33 (2013) 361-371.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Pm-saturated graphs with minimum size
Autorzy:: Dudek, A.
Wojda, A.P.
Tematy:: graph
saturated graph
extremal graph; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/2050147.pdf Link otwiera się w nowym oknie
Opis:: By Pm we denote a path of order m. A graph G is saidto be P$\text{}_{m}$ - saturated if G has no subgraph isomorphic to P$\text{}_{m}$ and adding any new edge to G creates a Pm in G. In 1986 L. Kaszonyi and Zs. Tuza considered the following problem: for given m and n find the minimum size $sat(n; P\text{}_{m}$) of P$\text{}_{m}$-saturated graph and characterize the graphs of $Sat(n; P\text{}_{m}$) - the set of P$\text{}_{m}$-saturated graphs of minimum size. They have solved this problem for $n \geq a_{m}$ where $$ a_{m} = \begin{cases} 3 \cdot 2^{k-1} - 2~~\text{if}~m = 2k,k~~~~~~~\\ 2^{k+1} - 2~~~~~~\text{if}~m = 2k + 1, k \geq 2 \end{cases} $$ We define $$ b_{m} = \begin{cases} 3 \cdot 2^{k-2}~~~~~~~\text{if}~m = 2k,k \geq 3 \\ 3 \cdot 2 ^{k-1} - 1~~\text{if}~m = 2k + 1,k \geq 3 \end{cases} $$ and give $sat(n; P\text{}_{m}$) and $Sat(n; P\text{}_{m})$ for $m \geq 6$ and $b_{m} \leq n < a_{m}$
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: The edge C₄ graph of some graph classes
Autorzy:: Menon, Manju
Vijayakumar, A.
Tematy:: edge C₄ graph
threshold graph
block graph
geodetic graph
weakly geodetic graph; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/744285.pdf Link otwiera się w nowym oknie
Opis:: The edge C₄ graph of a graph G, E₄(G) is a graph whose vertices are the edges of G and two vertices in E₄(G) are adjacent if the corresponding edges in G are either incident or are opposite edges of some C₄. In this paper, we show that there exist infinitely many pairs of non isomorphic graphs whose edge C₄ graphs are isomorphic. We study the relationship between the diameter, radius and domination number of G and those of E₄(G). It is shown that for any graph G without isolated vertices, there exists a super graph H such that C(H) = G and C(E₄(H)) = E₄(G). Also we give forbidden subgraph characterizations for E₄(G) being a threshold graph, block graph, geodetic graph and weakly geodetic graph.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: On the Intersection Graphs Associeted to Posets
Autorzy:: Afkhami, M.
Khashyarmanesh, K.
Shahsavar, F.
Tematy:: poset
intersection graph
split graph
planar graph
outerplanar graph; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/55795354.pdf Link otwiera się w nowym oknie
Opis:: Let (P, ≤) be a poset with the least element 0. The intersection graph of ideals of P, denoted by G(P), is a graph whose vertices are all nontrivial ideals of P and two distinct vertices I and J are adjacent if and only if I ∩ J ≠ {0}. In this paper, we study the planarity and outerplanarity of the intersection graph G(P). Also, we determine all posets with split intersection graphs.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 6.

Tytuł:: Clique graph representations of ptolemaic graphs
Autorzy:: McKee, Terry
Tematy:: Ptolemaic graph
clique graph
chordal graph
clique tree
graph representation; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/744102.pdf Link otwiera się w nowym oknie
Opis:: A graph is ptolemaic if and only if it is both chordal and distance-hereditary. Thus, a ptolemaic graph G has two kinds of intersection graph representations: one from being chordal, and the other from being distance-hereditary. The first of these, called a clique tree representation, is easily generated from the clique graph of G (the intersection graph of the maximal complete subgraphs of G). The second intersection graph representation can also be generated from the clique graph, as a very special case of the main result: The maximal Pₙ-free connected induced subgraphs of the p-clique graph of a ptolemaic graph G correspond in a natural way to the maximal $P_{n+1}$-free induced subgraphs of G in which every two nonadjacent vertices are connected by at least p internally disjoint paths.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 7.

Tytuł:: On Singular Signed Graphs with Nullspace Spanned by a Full Vector: Signed Nut Graphs
Autorzy:: Bašić, Nino
Fowler, Patrick W.
Pisanski, Tomaž
Sciriha, Irene
Tematy:: signed graph
nut graph
singular graph
graph spectrum
Fowler construction
sign-balanced graph
sign-unbalanced graph
cocktail-party graph; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/32222533.pdf Link otwiera się w nowym oknie
Opis:: A signed graph has edge weights drawn from the set {+1, −1}, and is sign-balanced if it is equivalent to an unsigned graph under the operation of sign switching; otherwise it is sign-unbalanced. A nut graph has a one dimensional kernel of the 0-1 adjacency matrix with a corresponding eigenvector that is full. In this paper we generalise the notion of nut graphs to signed graphs. Orders for which regular nut graphs with all edge weights +1 exist have been determined recently for the degrees up to 12. By extending the definition to signed graphs, we here find all pairs (ρ, n) for which a ρ-regular nut graph (sign-balanced or sign-unbalanced) of order n exists with ρ ≤ 11. We devise a construction for signed nut graphs based on a smaller ‘seed’ graph, giving infinite series of both sign-balanced and sign-unbalanced ρ -regular nut graphs. Orders for which a regular nut graph with ρ = n − 1 exists are characterised; they are sign-unbalanced with an underlying graph K_n for which n ≡ 1 (mod 4). Orders for which a regular sign-unbalanced nut graph with ρ = n − 2 exists are also characterised; they have an underlying cocktail-party graph CP(n) with even order n ≥ 8.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 8.

Tytuł:: (H,k) stable graphs with minimum size
Autorzy:: Dudek, Aneta
Szymański, Artur
Zwonek, Małgorzata
Tematy:: graph
stable graph; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743537.pdf Link otwiera się w nowym oknie
Opis:: Let us call a G (H,k) graph vertex stable if it contains a subgraph H ever after removing any of its k vertices. By Q(H,k) we will denote the minimum size of an (H,k) vertex stable graph. In this paper, we are interested in finding Q(₃,k), Q(₄,k), $Q(K_{1,p},k)$ and Q(Kₛ,k).
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 9.

Tytuł:: Digraphs with isomorphic underlying and domination graphs: connected $UG^c(d)$
Autorzy:: Factor, Kim
Langley, Larry
Tematy:: domination graph
domination
graph isomorphism
underlying graph; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743665.pdf Link otwiera się w nowym oknie
Opis:: The domination graph of a directed graph has an edge between vertices x and y provided either (x,z) or (y,z) is an arc for every vertex z distinct from x and y. We consider directed graphs D for which the domination graph of D is isomorphic to the underlying graph of D. We demonstrate that the complement of the underlying graph must have k connected components isomorphic to complete graphs, paths, or cycles. A complete characterization of directed graphs where k = 1 is presented.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 10.

Tytuł:: On An Extremal Problem In The Class Of Bipartite 1-Planar Graphs
Autorzy:: Czap, Július
Przybyło, Jakub
Škrabuľáková, Erika
Tematy:: 1-planar graph
bipartite graph
graph size; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31341143.pdf Link otwiera się w nowym oknie
Opis:: A graph G = (V, E) is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. In this paper, we study bipartite 1-planar graphs with prescribed numbers of vertices in partite sets. Bipartite 1-planar graphs are known to have at most 3n − 8 edges, where n denotes the order of a graph. We show that maximal-size bipartite 1-planar graphs which are almost balanced have not significantly fewer edges than indicated by this upper bound, while the same is not true for unbalanced ones. We prove that the maximal possible size of bipartite 1-planar graphs whose one partite set is much smaller than the other one tends towards 2n rather than 3n. In particular, we prove that if the size of the smaller partite set is sublinear in n, then |E| = (2 + o(1))n, while the same is not true otherwise.
Dostawca treści:: Biblioteka Nauki

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