On (a, D)-Antimagic Labelings Of Generalized Petersen Grapgs And Radio Number Of P₂□P_n

Graph labeling is an important part of graph theory. Accordingt to different applications, many variations of graph labelings are evolved. Combining the computer algorithm with mathematical proof, two classes of graph labelings: antimagic labeling and radio labeling are researched in this thesis.Magic labeling is motivated from magic square in number theory and divided into two categoties: magic and antimagic. (a, d)- antimagic labeling is one class of antimagic labelings. In this thesis, (a, d) - antimagic labeling of the generalized Petersen graph P(n,k) is studied. It is proved that the conjecture proposed by Baca and Miller when k = 2is true, that is, the generalized Petersen graph P(n,2) is ((?), 3) - antimagic forn≡2(mod 4), n≥10.Radio labeling (Multi-level distance labeling) is motivated by the effective channel assignment problem that each base station does not interferent from another introduced byChantrand et al. In this paper, the radio number of P₂â–¡P_n is researched. By graph labeling algorithm and mathematical proof, the lower bound and upper bound of radio labeling number of P₂â–¡P_n is proved, thus the radio labeling number is determined, that is,...