Results 21 to 30 of about 1,099 (89)
A note on the k‐domination number of a graph
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 1, Page 205-206, 1990., 1989 The k‐domination number of a graph G = G(V, E), γk(G), is the least cardinality of a set X ⊂ V such that any vertex in VX is adjacent to at least k vertices of X. Extending a result of Cockayne, Gamble and Shepherd [4], we prove that if , n ≥ 1, k ≥ 1 then, , where p is the order of G.
Y. Caro, Y. Roditty
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Hyper-Wiener indices of polyphenyl chains and polyphenyl spiders
Open Mathematics, 2019 Let G be a connected graph and u and v two vertices of G. The hyper-Wiener index of graph G is WW(G)=12∑u,v∈V(G)(dG(u,v)+dG2(u,v))$\begin{array}{} WW(G)=\frac{1}{2}\sum\limits_{u,v\in V(G)}(d_{G}(u,v)+d^{2}_{G}(u,v)) \end{array}$, where dG(u, v) is the ...
Wu Tingzeng, Lü Huazhong
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On the discrepancy of coloring finite sets
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 4, Page 825-827, 1990., 1990 Given a subset S of {1, …, n} and a map X : {1, …, n} → {−1, 1}, (i.e. a coloring of {1, …, n} with two colors, say red and blue) define the discrepancy of S with respect to X to be dX(S)=|∑i∈SX(i)| (the difference between the reds and blues on S).
D. Hajela
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Large butterfly Cayley graphs and digraphs [PDF]
, 2017 We present families of large undirected and directed Cayley graphs whose construction is related to butterfly networks. One approach yields, for every large $k$ and for values of $d$ taken from a large interval, the largest known Cayley graphs and ...
Bevan, David
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A regular graph of girth 6 and valency 11
International Journal of Mathematics and Mathematical Sciences, Volume 9, Issue 3, Page 561-565, 1986., 1986 Let f(11, 6) be the number of vertices of an (11, 6)‐cage. By giving a regular graph of girth 6 and valency 11, we show that f(11, 6) ≤ 240. This is the best known upper bound for f(11, 6).
P. K. Wong
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A note on the problem of finding a (3, 9)‐cage
International Journal of Mathematics and Mathematical Sciences, Volume 8, Issue 4, Page 817-820, 1985., 1985 In this paper, we discuss The poblem of finding a (3, 9)‐cage. A hamiltonian graph with girth 9 and 54 vertices is given. Except four vertices, each of the remaining vertices of this graph has valency Three. This graph is obtained with the aid of a computer.
P. K. Wong
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International Journal of Mathematics and Mathematical Sciences, Volume 5, Issue 3, Page 553-564, 1982., 1982 A graph is subeulerian if it is spanned by an eulerian supergraph. Boesch, Suffel and Tindell have characterized the class of subeulerian graphs and determined the minimum number of additional lines required to make a subeulerian graph eulerian. In this paper, we consider the related notion of a subsemi‐eulerian graph, i.e.
Charles Suffel +3 more
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Minimally Strong Subgraph (k,ℓ)-Arc-Connected Digraphs
Discussiones Mathematicae Graph Theory, 2022 Let D = (V,A) be a digraph of order n, S a subset of V of size k and 2 ≤ k ≤ n. A subdigraph H of D is called an S-strong subgraph if H is strong and S ⊆ V (H). Two S-strong subgraphs D1 and D2 are said to be arc-disjoint if A(D1) ∩ A(D2) = ∅.
Sun Yuefang, Jin Zemin
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Exact solutions to the Erdős-Rothschild problem
Forum of Mathematics, SigmaLet $\boldsymbol {k} := (k_1,\ldots ,k_s)$ be a sequence of natural numbers. For a graph G, let $F(G;\boldsymbol {k})$ denote the number of colourings of the edges of G with colours $1,\dots ,s$ such that, for every $c \in \{1 ...
Oleg Pikhurko, Katherine Staden
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On extremal numbers of the triangle plus the four-cycle
Forum of Mathematics, SigmaFor a family $\mathcal {F}$ of graphs, let ${\mathrm {ex}}(n,\mathcal {F})$ denote the maximum number of edges in an n-vertex graph which contains none of the members of $\mathcal {F}$ as a subgraph.
Jie Ma, Tianchi Yang
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