New Infinite Families of 2-Edge-Balanced Graphs
نویسندگان
چکیده
A graph G of order n is called t-edge-balanced if G satisfies the property that there exists a positive λ for which every graph of order n and size t is contained in exactly λ distinct subgraphs of Kn isomorphic to G. We call λ the index of G. In this article, we obtain new infinite families of 2-edge-balanced graphs. C ⃝ 2013 Wiley Periodicals, Inc. J. Combin. Designs 22: 291–305, 2014
منابع مشابه
Distance-balanced graphs: Symmetry conditions
A graph X is said to be distance–balanced if for any edge uv of X , the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. A graph X is said to be strongly distance–balanced if for any edge uv of X and any integer k, the number of vertices at distance k from u and at distance k+1 from v is equal to the number of vertices at distance k + 1 from u a...
متن کاملA note on Fouquet-Vanherpe’s question and Fulkerson conjecture
The excessive index of a bridgeless cubic graph $G$ is the least integer $k$, such that $G$ can be covered by $k$ perfect matchings. An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless cubic graph has excessive index at most five. Clearly, Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5, so Fouquet and Vanherpe as...
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 کاملOn distance-balanced graphs
It is shown that the graphs for which the Szeged index equals ‖G‖·|G| 2 4 are precisely connected, bipartite, distance-balanced graphs. This enables to disprove a conjecture proposed in [Some new results on distance-based graph invariants, European J. Combin. 30 (2009) 1149–1163]. Infinite families of counterexamples are based on the Handa graph, the Folkman graph, and the Cartesian product of ...
متن کاملOn the edge-connectivity of C_4-free graphs
Let $G$ be a connected graph of order $n$ and minimum degree $delta(G)$.The edge-connectivity $lambda(G)$ of $G$ is the minimum numberof edges whose removal renders $G$ disconnected. It is well-known that$lambda(G) leq delta(G)$,and if $lambda(G)=delta(G)$, then$G$ is said to be maximally edge-connected. A classical resultby Chartrand gives the sufficient condition $delta(G) geq frac{n-1}{2}$fo...
متن کامل