A note on incidence graphs. (English) Zbl 1267.05200
Balakrishnan, R. (ed.) et al., International conference on graph theory and its applications. Papers from the conference, Coimbatore, India, December 11–13, 2008. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 33, 87-93 (2009).
Summary: An incidence graph of a given graph \(G\), denoted by \(I(G)\), has its vertex set \(V(I(G))=\{(ve):v\in V(G),e\in E(G)\text{ and }v\text{ is incident to }e\text{ in }G\}\) such that the pair \((ue)(vf)\) of vertices \((ue),(vf)\in V(I(G))\) is an edge of \(I(G)\) if and only if there exists at least one case of \(u=v\), \(e=f\), \(uv=e\) or \(uv=f\). Incidence graphs were studied by Z. Zhong-fu et al. [Ars Comb. 87, 213–223 (2008; Zbl 1224.05202)]. The origin of incidence graphs can be traced to a paper titled “Incidence and strong edge colorings of graphs” by R. A. Brualdi et al. [Discrete Math. 122, No. 1–3, 51–58 (1993; Zbl 0790.05026)]. In this paper, we investigate domination and related parameters in incidence graphs.
For the entire collection see [Zbl 1239.05003].
For the entire collection see [Zbl 1239.05003].
MSC:
| 05C69 | Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) |
References:
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