Browsing by Subject "dense graphs"

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Access status: Open Access ,
M₂-edge colorings of dense graphs
(2016) Ivančo, Jaroslav
An edge coloring $\varphi$ of a graph $G$ is called an $\mathrm{M}_i$-edge coloring if $|\varphi(v)|\leq i$ for every vertex $v$ of $G$, where $\varphi(v)$ is the set of colors of edges incident with $v$. Let $\mathcal{K}_i(G)$ denote the maximum number of colors used in an $\mathrm{M}_i$-edge coloring of $G$. In this paper we establish some bounds of $\mathcal{K}_2(G)$, present some graphs achieving the bounds and determine exact values of $\mathcal{K}_2(G)$ for dense graphs.
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.