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The multi--intersection number of a graph

西安电子科技大学学报 1990年第4期17卷 22-25页

作者： frank harary Department of Computer Scicnce New Mexico State University USA

The intersection number, in (G), has been defined as the minimumcardinality of a set S which has n different subsets S_i such that each S_i can beassigned to the node v_i of G and nodes v_i, v_j are adjacent if and onlyif S_i∩S_j ≠0. We introduce the multiset intersection number min (G), defined similarly exceptthat multisets with elements in S may now be assigned to the nodes of G. Weprove that min (G) equals the smallest number ofcliques of G whose union is G.

关键词： Intersection graph number

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FINITE GR0UP TABLE ACHIEVEMENT GAMES

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工程数学学报 1989年第3期 43-47页

作者： Jozsef Denes,frank harary University of Surrey Guildfovd England. Nev Mexico State University Las Cruces USA.

Latin square achievement games were iutroduced and resolved by hararyand Leary. In those games, a legal move places a number k between l andn in a cell of a spuare matrix for which no other cell in the same row orcolumn already contains k. The last player who can make a legal *** we introduce group table achievement games. As every finite grouptable is a latin square satisfying the "quadrangle criterion", a legalmove in this game must also satisfy the above condition. Again, the lastplayer who moves legally is the winner. We analyze group table achiementgames for order n≤6.

关键词： FINITE GR0UP TABLE ACHIEVEMENT GAMES

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LINE COLORED TREES WITH EXTENDABLE AUTOMORPHISMS

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数学物理学报 1982年第1期 105-110页

作者： Georg Gati,frank harary,Robert W. Robinson Institut fur Informatik ETH Zurich 5] Austria. Supported by Swiss National Science Foundation Grants Nos. Switzerland. Present address: Institut fur Informatik Universitat Wien Ovrseas Fellow(1980-81) Churchill College University of Cambridge England.Present address: Department of Mathematics University of Michigan Ann Arbor MI 48109 U.S.A. University of Newcastle New South Wales 2308 Australia. Temporary address: Department of Mathematics University of Michigan Ann Arbor MI 48109 20] U.S.A. until Jan.

An E-tree is a rooted line-colored tree such that every automorphism of a subtree contain-s ing the root can be extended to an automorphism of the entire tree. When only one color i used, E-trees correspond both to achiral planted trees and to partitions with successively divisible parts. The exact numbers of E-trees with n points and colors from a store of c are found, with and without the restriction that each color should be used at least one. Asymptotic formulas for these quantities are discussed for c fixed and n→∞.

关键词： tree root LINE COLORED TREES WITH EXTENDABLE AUTOMORPHISMS

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