Browsing by Subject "regular graphs"

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Access status: Open Access ,
On edge product cordial graphs
(Wydawnictwa AGH, 2019) Ivančo, Jaroslav
An edge product cordial labeling is a variant of the well-known cordial labeling. In this paper we characterize graphs admitting an edge product cordial labeling. Using this characterization we investigate the edge product cordiality of broad classes of graphs, namely, dense graphs, dense bipartite graphs, connected regular graphs, unions of some graphs, direct products of some bipartite graphs, joins of some graphs, maximal $k$-degenerate and related graphs, product cordial graphs.
Access status: Open Access ,
Signed star (k,k)-domatic number of a graph
(2014) Sheikholeslami, Seyed Mahmoud; Volkmann, Lutz
Let $G$ be a simple graph without isolated vertices with vertex set $V(G)$ and edge set $E(G)$ and let $k$ be a positive integer. A function $f:E(G)\longrightarrow \{-1, 1\}$ is said to be a signed star $k$-dominating function on $G$ if $\sum_{e\in E(v)}f(e)\ge k$ for every vertex $v$ of $G$, where $E(v)=\{uv\in E(G)\mid u\in N(v)\}$. A set $\{f_1,f_2,\ldots,f_d\}$ of signed star $k$-dominating functions on $G$ with the property that $\sum_{i=1}^df_i(e)\le k$ for each $e\in E(G)$, is called a signed star $(k,k)$-dominating family (of functions) on $G$. The maximum number of functions in a signed star $(k,k)$-dominating family on $G$ is the signed star $(k,k)$-domatic number of $G$, denoted by $d^{(k,k)}_{SS}(G)$. In this paper we study properties of the signed star $(k,k)$-domatic number $d^{(k,k)}_{SS}(G)$. In particular, we present bounds on $d_{SS}^{(k,k)}(G)$, and we determine the signed $(k,k)$-domatic number of some regular graphs. Some of our results extend these given by Atapour, Sheikholeslami, Ghameslou and Volkmann [Signed star domatic number of a graph, Discrete Appl. Math. 158 (2010), 213-218] for the signed star domatic number.