Relations between $(\kappa ,\tau )$-regular sets and star complements

Milica Anđelić; Domingos M. Cardoso; Slobodan K. Simić

Displaying similar documents to “Relations between $(κ, τ)$ -regular sets and star complements”

On graphs with the largest Laplacian index

Bo Lian Liu, Zhibo Chen, Muhuo Liu (2008)

Czechoslovak Mathematical Journal

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Let $G$ be a connected simple graph on $n$ vertices. The Laplacian index of $G$ , namely, the greatest Laplacian eigenvalue of $G$ , is well known to be bounded above by $n$ . In this paper, we give structural characterizations for graphs $G$ with the largest Laplacian index $n$ . Regular graphs, Hamiltonian graphs and planar graphs with the largest Laplacian index are investigated. We present a necessary and sufficient condition on $n$ and $k$ for the existence of a $k$ -regular graph $G$ of order $n$ with the...

Results on $F$ -continuous graphs

Anna Draganova (2009)

Czechoslovak Mathematical Journal

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For any nontrivial connected graph $F$ and any graph $G$ , the of a vertex $v$ in $G$ is the number of copies of $F$ in $G$ containing $v$ . $G$ is called if and only if the $F$ -degrees of any two adjacent vertices in $G$ differ by at most 1; $G$ is if the $F$ -degrees of all vertices in $G$ are the same. This paper classifies all $P_{4}$ -continuous graphs with girth greater than 3. We show that for any nontrivial connected graph $F$ other than the star $K_{1, k}$ , $k \geq 1$ , there exists a regular graph that is not $F$ -continuous. If...

Cores and shells of graphs

Allan Bickle (2013)

Mathematica Bohemica

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The $k$ -core of a graph $G$ , $C_{k} (G)$ , is the maximal induced subgraph $H \subseteq G$ such that $δ (G) \geq k$ , if it exists. For $k > 0$ , the $k$ -shell of a graph $G$ is the subgraph of $G$ induced by the edges contained in the $k$ -core and not contained in the $(k + 1)$ -core. The core number of a vertex is the largest value for $k$ such that $v \in C_{k} (G)$ , and the maximum core number of a graph, $\hat{C} (G)$ , is the maximum of the core numbers of the vertices of $G$ . A graph $G$ is $k$ -monocore if $\hat{C} (G) = δ (G) = k$ . This paper discusses some basic results on the structure of $k$ -cores and...

Equienergetic self-complementary graphs

G. Indulal, A. Vijayakumar (2008)

Czechoslovak Mathematical Journal

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In this paper equienergetic self-complementary graphs on $p$ vertices for every $p = 4 k$ , $k \geq 2$ and $p = 24 t + 1$ , $t \geq 3$ are constructed.

Displaying similar documents to “Relations between ( κ , τ ) -regular sets and star complements”

On graphs with the largest Laplacian index

Results on F -continuous graphs

Cores and shells of graphs

Equienergetic self-complementary graphs

Displaying similar documents to “Relations between $(κ, τ)$ -regular sets and star complements”

Results on $F$ -continuous graphs