The strongly distance-balanced property of the generalized Petersen graphs
نویسندگان
چکیده
منابع مشابه
A Note on the Distance-Balanced Property of Generalized Petersen Graphs
A graph G is said to be distance-balanced if for any edge uv of G, the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Let GP (n, k) be a generalized Petersen graph. Jerebic, Klavžar, and Rall [Distance-balanced graphs, Ann. Comb. 12 (2008) 71–79] conjectured that: For any integer k > 2, there exists a positive integer n0 such that the GP (n, k...
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A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...
متن کاملRemarks on Distance-Balanced Graphs
Distance-balanced graphs are introduced as graphs in which every edge uv has the following property: the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. In this paper, we study the conditions under which some graph operations produce a distance-balanced graph.
متن کاملStrongly distance-balanced graphs and graph products1
A graph G is strongly distance-balanced if for every edge uv of G and every i ≥ 0 the number of vertices x with d(x, u) = d(x, v)−1 = i equals the number of vertices y with d(y, v) = d(y, u) − 1 = i. It is proved that the strong product of graphs is strongly distance-balanced if and only if both factors are strongly distancebalanced. It is also proved that connected components of the direct pro...
متن کاملAll generalized Petersen graphs are unit-distance graphs
In 1950 a class of generalized Petersen graphs was introduced by Coxeter and around 1970 popularized by Frucht, Graver and Watkins. The family of I-graphs mentioned in 1988 by Bouwer et al. represents a slight further albeit important generalization of the renowned Petersen graph. We show that each I-graph I(n, j, k) admits a unit-distance representation in the Euclidean plane. This implies tha...
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ژورنال
عنوان ژورنال: Ars Mathematica Contemporanea
سال: 2009
ISSN: 1855-3974,1855-3966
DOI: 10.26493/1855-3974.75.895