Diameter and Travers ability of PAN Critical
Graphs

J. Suresh Kumar

doi:https://doi.org/10.14445/22315373/IJMTT-V52P564

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 52 | Number 7 | Year 2017 | Article Id. IJMTT-V52P564 | DOI : https://doi.org/10.14445/22315373/IJMTT-V52P564

Diameter and Travers ability of PAN Critical Graphs

J. Suresh Kumar

Abstract

A pseudo-complete coloring of a graph G is an assignment of colors to the vertices of G such that for any two distinct colors, there existadjacent vertices having those colors. The maximum number of colors used in a pseudocomplete coloring of G is called the pseudoachromatic number of G and is denoted by𝜓𝑠(𝐺). A graph G is called edge critical if 𝜓𝑠(𝐺 − 𝑒)<𝜓𝑠 (𝐺)for any edge e of G. A graph G is called vertex critical if 𝜓𝑠 𝐺 − 𝑣 <. 𝜓𝑠(𝐺)for every vertex v of G. These graphs are generally called as pseudoachromatic number critical graphs (shortly as PAN Critical graphs). In this paper, we investigate the properties of these critical graphs.

Keywords

Pseudo-complete coloring, Pseudoachromatic number, k-edge critical graph, kvertex critical graph.

References

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Citation :

J. Suresh Kumar, "Diameter and Travers ability of PAN Critical Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 52, no. 7, pp. 449-451, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V52P564