A smallest graph of girth 10 and valency 3
نویسندگان
چکیده
منابع مشابه
On the smallest 3-cop win graph
In the game of cops and robbers on a graph G = (V,E), k cops try to catch a robber. On the cop turn, each cop may move to a neighboring vertex or remain in place. On the robber’s turn, he moves similarly. The cops win if there is some time at which a cop is at the same vertex as the robber. Otherwise, the robber wins. The minimum number of cops required to catch the robber is called the cop num...
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We describe two computational methods for the construction of cubic graphs with given girth. These were used to produce two independent proofs that the (3, 9)-cages, defined as the smallest cubic graphs of girth 9, have 58 vertices. There are exactly 18 such graphs. We also show that cubic graphs of girth 11 must have at least 106 vertices and cubic graphs of girth 13 must have at least 196 ver...
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In the game of cops and robbers on a graph G = (V,E), k cops try to catch a robber. On the cop turn, each cop may move to a neighboring vertex or remain in place. On the robber’s turn, he moves similarly. The cops win if there is some time at which a cop is at the same vertex as the robber. Otherwise, the robber wins. The minimum number of cops required to catch the robber is called the cop num...
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We construct a graph of order 384, the smallest known trivalent graph of girth 14. AMS Subject Classifications: 05D25, 05D35 In this note we use a construction technique that can be viewed as a kind of generalized Cayley graph. The vertex set V of such a graph consists of the elements in multiple copies of some finite group G. The action of G on V is determined by the regular action on each of ...
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The annihilating-ideal graph of a commutative ring $R$ is denoted by $AG(R)$, whose vertices are all nonzero ideals of $R$ with nonzero annihilators and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ=0$. In this article, we completely characterize rings $R$ when $gr(AG(R))neq 3$.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1980
ISSN: 0095-8956
DOI: 10.1016/0095-8956(80)90046-5