PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 33(47), pp. 227234 (1983) 

FINITENESS OF SPECTRA OF GRAPHS OBTAINED BY SOME OPERATIONS ON INFINITE GRAPHSAleksandar TorgasevMatematicki fakultet, Beograd, YugoslaviaAbstract: In this paper we consider some unary and binary operations on infinite graphs, and we investigate when the spectrum of the resulting graph is finite. \par In particular, we consider the induced subgraphs of an infinite graph, relabeling of its vertices, the complementary graph, the union, Cartesian product, complete product and direct sum of two infinite graphs, the line graph and the total graph of a graph. \par For some of these operations we find that the spectrum of the graph so obtained is always infinite (direct sum, line and total graph). Among other things, we show that finiteness of the spectrum of an infinite graph does not change by any relabeling of its vertices. Keywords: Connected infinite graph, operation on infinite graphs, spectrum of a graph, finiteness of the spectrum Classification (MSC2000): 05C50; 47A65 Full text of the article:
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