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Start Over Subject complete bipartite graph

1. Balanced path decomposition of $\lambda K_{n,n}$ and $\lambda K^*_{n,n}$

Creator:
Lee, Hung Chih and Lin, Chiang
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
path decomposition, balanced decomposition, and complete bipartite graph
Language:
English
Description:
Let $P_k$ denote a path with $k$ edges and $łK_{n,n}$ denote the $ł$-fold complete bipartite graph with both parts of size $n$. In this paper, we obtain the necessary and sufficient conditions for $łK_{n,n}$ to have a balanced $P_k$-decomposition. We also obtain the directed version of this result.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Decomposition of complete bipartite even graphs into closed trails

Creator:
Horňák, Mirko and Woźniak, Mariusz
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
complete bipartite graph, closed trail, and arbitrarily decomposable graph
Language:
English
Description:
We prove that any complete bipartite graph $K_{a,b}$, where $a,b$ are even integers, can be decomposed into closed trails with prescribed even lengths.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Signed total domination number of a graph

Creator:
Zelinka, Bohdan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
signed total dominating function, signed total domination number, regular graph, circuit, complete graph, complete bipartite graph, and Cartesian product of graphs
Language:
English
Description:
The signed total domination number of a graph is a certain variant of the domination number. If $v$ is a vertex of a graph $G$, then $N(v)$ is its oper neighbourhood, i.e. the set of all vertices adjacent to $v$ in $G$. A mapping $f: V(G) \rightarrow \lbrace -1, 1\rbrace $, where $V(G)$ is the vertex set of $G$, is called a signed total dominating function (STDF) on $G$, if $\sum _{x \in N(v)} f(x) \ge 1$ for each $v \in V(G)$. The minimum of values $\sum _{x \in V(G)} f(x)$, taken over all STDF’s of $G$, is called the signed total domination number of $G$ and denoted by $\gamma _{\mathrm st}(G)$. A theorem stating lower bounds for $\gamma _{\mathrm st}(G)$ is stated for the case of regular graphs. The values of this number are found for complete graphs, circuits, complete bipartite graphs and graphs on $n$-side prisms. At the end it is proved that $\gamma _{\mathrm st}(G)$ is not bounded from below in general.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public