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Displaying similar documents to “Degree sequences of graphs containing a cycle with prescribed length”

A Havel-Hakimi type procedure and a sufficient condition for a sequence to be potentially S r , s -graphic

Jian Hua Yin (2012)

Czechoslovak Mathematical Journal

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The split graph K r + K s ¯ on r + s vertices is denoted by S r , s . A non-increasing sequence π = ( d 1 , d 2 , ... , d n ) of nonnegative integers is said to be potentially S r , s -graphic if there exists a realization of π containing S r , s as a subgraph. In this paper, we obtain a Havel-Hakimi type procedure and a simple sufficient condition for π to be potentially S r , s -graphic. They are extensions of two theorems due to A. R. Rao (The clique number of a graph with given degree sequence, Graph Theory, Proc. Symp., Calcutta 1976, ISI Lect. Notes...

Potentially K m - G -graphical sequences: A survey

Chunhui Lai, Lili Hu (2009)

Czechoslovak Mathematical Journal

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The set of all non-increasing nonnegative integer sequences π = ( d ( v 1 ) , d ( v 2 ) , ⋯ , d ( v n ) ) is denoted by NS n . A sequence π ∈ NS n is said to be graphic if it is the degree sequence of a simple graph G on n vertices, and such a graph G is called a realization of π . The set of all graphic sequences in NS n is denoted by GS n . A graphical sequence π is potentially H -graphical if there is a realization of π containing H as a subgraph, while π is forcibly H -graphical if every realization of π contains H as a subgraph. Let K k denote...

Wiener and vertex PI indices of the strong product of graphs

K. Pattabiraman, P. Paulraja (2012)

Discussiones Mathematicae Graph Theory

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The Wiener index of a connected graph G, denoted by W(G), is defined as ½ ∑ u , v ∈ V ( G ) d G ( u , v ) . Similarly, the hyper-Wiener index of a connected graph G, denoted by WW(G), is defined as ½ W ( G ) + ¼ ∑ u , v ∈ V ( G ) d ² G ( u , v ) . The vertex Padmakar-Ivan (vertex PI) index of a graph G is the sum over all edges uv of G of the number of vertices which are not equidistant from u and v. In this paper, the exact formulae for Wiener, hyper-Wiener and vertex PI indices of the strong product G ⊠ K m ₀ , m ₁ , . . . , m r - 1 , where K m ₀ , m ₁ , . . . , m r - 1 is the complete multipartite graph with partite sets...

Tight bounds for the dihedral angle sums of a pyramid

Sergey Korotov, Lars Fredrik Lund, Jon Eivind Vatne (2023)

Applications of Mathematics

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We prove that eight dihedral angles in a pyramid with an arbitrary quadrilateral base always sum up to a number in the interval ( 3 π , 5 π ) . Moreover, for any number in ( 3 π , 5 π ) there exists a pyramid whose dihedral angle sum is equal to this number, which means that the lower and upper bounds are tight. Furthermore, the improved (and tight) upper bound 4 π is derived for the class of pyramids with parallelogramic bases. This includes pyramids with rectangular bases, often used in finite element mesh generation...

A generalization of the Keller-Segel system to higher dimensions from a structural viewpoint

Fujie, Kentarou, Senba, Takasi

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We consider initial boundary problems of a two-chemical substances chemotaxis system. In the four-dimensional setting, it was shown that solutions exist globally in time and remain bounded if the total mass is less than ( 8 π ) 2 , whereas the solution emanating from some initial data of large magnitude may blows up. This result can be regarded as a generalization of the well-known 8 π problem in the Keller–Segel system to higher dimensions. We will compare mathematical structures of the Keller–Segel...