A Note on k-Step Hamiltonian Graphs

N. Abd Aziz | Nader Jafari Rad | H. Kamarulhaili | R. Hasni

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=116479
Date :  2019/04/24
Publish in :    Malaysian Journal of Mathematical Sciences

Link :  http://einspem.upm.edu.my/journal/fullpaper/vol13no1/7.20Roslan20Hasni.pdf
Keywords :,k-SH graphs,independence,Hamiltonian

Abstract :

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For a given integer k, a given graph G on n vertices is called k-step Hamiltonian (or just k-SH) if the vertices of G can be labeled as v1; v2; :::; vn such that d(v1; vn) = k and d(vi; vi+1) = k for each i = 1; 2; :::; n 􀀀 1. In this paper, we present a construction namely B-construction that produces a (k+i)-SH graph from any k-SH graph G for every positive integer i  1.