Results 31 to 40 of about 234 (95)
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
wiley +1 more source
New upper bounds on the order of cages
Electronic Journal of Combinatorics, 1996 Let k≥2 and g≥3 be integers. A (k,g)-graph is a k-regular graph with girth (length of a smallest cycle) exactly g. A (k,g)-cage is a (k,g)-graph of minimum order. Let v(k,g) be the order of a (k,g)-cage.
F. Lazebnik, V. Ustimenko, A. Woldar
semanticscholar +1 more source
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
wiley +1 more source
An isoperimetric theorem on the cube and the Kintchine-Kahane inequalities
, 1988 For vectors xi,..., xn in a Banach space, we bound the deviation of || ^2 a(x) — inf{||a: j/||2; 2/ € conv^}. THEOREM 1. Eexp((t>A/8) 0, we have Pn({4>A > t}) t}) when Pn(A) is given is known. The sets for which Pn({dA > t}) is maximum are identified in [
M. Talagrand
semanticscholar +1 more source
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
wiley +1 more source
ON TOPOLOGICAL PROPERTIES OF PLANE GRAPHS BY USING LINE OPERATOR ON THEIR SUBDIVISIONS
International Journal of Apllied Mathematics, 2018 In this paper, we will compute some topological indices such as Zagreb indices M1(G), M2(G), M3(G), Zagreb coindices M1(G), M1(G), M2(G), M2(G)), M2(G), hyper-Zagreb index HM(G), atom-bond connectivity index ABC(G), sum connectivity index χ(G ...
Mohamad Nazri Husin +4 more
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On the Sizes of (k, l)-Edge-Maximal r-Uniform Hypergraphs
Discussiones Mathematicae Graph Theory, 2023 Let H = (V, E) be a hypergraph, where V is a set of vertices and E is a set of non-empty subsets of V called edges. If all edges of H have the same cardinality r, then H is an r-uniform hypergraph; if E consists of all r-subsets of V, then H is a ...
Tian Yingzhi +3 more
doaj +1 more source
The upper bounds for multiplicative sum Zagreb index of some graph operations
, 2017 Let G be a simple graph with vertex set V(G) and edge set E(G). In [7], Eliasi et al. introduced the multiplicative sum Zagreb index of a graph G which is denoted by Π1(G) and is defined by Π1(G) = ∏ uv∈V (G) (dG(u)+dG(v)) .
Yasar Nacaroglu, A. D. Maden
semanticscholar +1 more source
Avoiding rainbow 2-connected subgraphs
Open Mathematics, 2017 While defining the anti-Ramsey number Erdős, Simonovits and Sós mentioned that the extremal colorings may not be unique. In the paper we discuss the uniqueness of the colorings, generalize the idea of their construction and show how to use it to ...
Gorgol Izolda
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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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