Cichacz-Przeniosło, Sylwia
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aktywny
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matematyka
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Systemy AGH
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Item type:Article, Access status: Open Access , Upper bounds on distance vertex irregularity strength of some families of graphs(Wydawnictwa AGH, 2022) Cichacz-Przeniosło, Sylwia; Görlich, Agnieszka; Semaničová-Feňovčíková, AndreaFor a graph $G$ its distance vertex irregularity strength is the smallest integer $k$ for which one can find a labeling $f: V(G)\to \{1, 2, \dots, k\}$ such that $\sum_{x\in N(v)}f(x)\neq \sum_{x\in N(u)}f(x)$ for all vertices $u,v$ of $G$, where $N(v)$ is the open neighborhood of v. In this paper we present some upper bounds on distance vertex irregularity strength of general graphs. Moreover, we give upper bounds on distance vertex irregularity strength of hypercubes and trees.Item type:Article, Access status: Open Access , Open trails in digraphs(2011) Cichacz-Przeniosło, Sylwia; Görlich, AgnieszkaIt has been shown in [S. Cichacz, A. Görlich, Decomposition of complete bipartite graphs into open trails, Preprint MD 022, (2006)] that any bipartite graph $K_{a,b}$, is decomposable into open trails of prescribed even lengths. In this article we consider the corresponding question for directed graphs. We show that the complete directed graphs $\overleftrightarrow{K}_n$ and $\overleftrightarrow{K}_{a,b}$ are arbitrarily decomposable into directed open trails.Item type:Article, Access status: Open Access , 2-splittable and cordial graphs(2010) Cichacz-Przeniosło, SylwiaE. Miller and G. E. Stevens proved in [E. Miller, G. E. Stevens, <i>Some graphs for which even size is sufficient for splittability</i>, Congressus Numerantium 173 (2005), 137–147] the existence of certain families of $2$-splittable caterpillars. In this paper we characterize other families of $2$-splittable caterpillars. Moreover, we show that for some of them there exists a friendly labeling inducing two isomorphic subgraphs.Item type:Article, Access status: Open Access , Minimum k-critical-bipartite graphs: the irregular case(Wydawnictwa AGH, 2026) Cichacz-Przeniosło, Sylwia; Görlich, Agnieszka; Suchan, KarolWe study the problem of finding a minimum \(k\)-critical-bipartite graph of order \((n,m)\): a bipartite graph \(G=(U,V;E)\), with \(|U|=n\), \(|V|=m\), and \(n\gt m\gt 1\), which is \(k\)-critical-bipartite, and the tuple \((|E|, \Delta_U, \Delta_V)\), where \(\Delta_U\) and \(\Delta_V\) denote the maximum degree in \(U\) and \(V\), respectively, is lexicographically minimum over all such graphs. \(G\) is \(k\)-critical-bipartite if deleting any set of at most \(k=n-m\) vertices from \(U\) yields \(G'\) that has a complete matching, i.e., a matching of size \(m\). Cichacz and Suchan solved the problem for biregular bipartite graphs. Here, we extend their results to bipartite graphs that are not biregular. We prove tight lower bounds on the connectivity of \(k\)-critical-bipartite graphs, and we show that \(k\)-critical-bipartite graphs are expander graphs.