diameter two graphs of minimum order with given degree set
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abstract
the degree set of a graph is the set of its degrees. kapoor et al. [degree sets for graphs, fund. math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. furthermore, the minimum order of such a graph is determined. a graph is 2-self- centered if its radius and diameter are two. in this paper for a given set of natural numbers greater than one, we determine the minimum order of a 2-self-centered graph with that degree set.
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mathematics interdisciplinary researchجلد ۱، شماره ۲، صفحات ۳۱۹-۳۲۵
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