Geodesic
Finiteness of Spectra of Graphs Obtained by some Operations on Infinite Graphs
Publications de l'Institut Mathématique, _N_S_33 (1983) no. 47, p. 227 .

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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. 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. 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.
Classification : 05C50 47A65
Keywords: Connected infinite graph, operation on infinite graphs, spectrum of a graph, finiteness of the spectrum 
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     author = {Aleksandar Torga\v{s}ev},
     title = {Finiteness of {Spectra} of {Graphs} {Obtained} by some {Operations} on {Infinite} {Graphs}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {227 },
     publisher = {mathdoc},
     volume = {_N_S_33},
     number = {47},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1983_N_S_33_47_a33/}
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Aleksandar Torgašev. Finiteness of Spectra of Graphs Obtained by some Operations on Infinite Graphs. Publications de l'Institut Mathématique, _N_S_33 (1983) no. 47, p. 227 . http://geodesic.mathdoc.fr/item/PIM_1983_N_S_33_47_a33/