Inequalities between distance-based graph polynomials
2006 ◽
Vol 133
(31)
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pp. 57-68
Keyword(s):
In a recent paper [ I. Gutman, Bull. Acad. Serbe Sci. Arts (Cl. Math. Natur) 131 (2005) 1-7], the Hosoya polynomial H = H(G,?) of a graph G, and two related distance-based polynomials H1 = H1(G, ?) and H2 = H2(G, ?) were examined. We now show that max-?H1 - ?2H, ?H1 - ?2H} ? H2 ? ?H1 - ??H holds for all graphs G and for all ? ? 0, where ? and ? are the smallest and greatest vertex degree in G. The answer to the question which of the terms ?H1 -?2H and ?H1 -?2H is greater, depends on the graph G and on the value of the variable ?. We find a number of particular solutions of this problem. AMS Mathematics Subject Classification (2000): 05C12, 05C05.
2014 ◽
Vol 0
(0)
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1995 ◽
Vol 45
(3-4)
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pp. 171-178
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2000 ◽
Vol 42
(1)
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pp. 97-113
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Keyword(s):
1990 ◽
Vol 4
(2)
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pp. 184-184
Keyword(s):
2004 ◽
Vol 166
(1)
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pp. 181-208
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2003 ◽
Vol 86
(2)
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pp. 327-357
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