منابع مشابه
Oriented diameter of graphs with diameter 3
In 1978, Chvátal and Thomassen proved that every 2-edge-connected graph with diameter 2 has an orientation with diameter at most 6. They also gave general bounds on the smallest value f(d) such that every 2-edge-connected graph G with diameter d has an orientation with diameter at most f(d). For d = 3, their general bounds reduce to 8 ≤ f(3) ≤ 24. We improve these bounds to 9 ≤ f(3) ≤ 11.
متن کاملOn Diameter of Line Graphs
The diameter of a connected graph $G$, denoted by $diam(G)$, is the maximum distance between any pair of vertices of $G$. Let $L(G)$ be the line graph of $G$. We establish necessary and sufficient conditions under which for a given integer $k geq 2$, $diam(L(G)) leq k$.
متن کاملEccentric Connectivity Index: Extremal Graphs and Values
Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine ...
متن کاملDiameter and connectivity of 3-arc graphs
An arc of a graph is an oriented edge and a 3-arc is a 4-tuple (v, u, x, y) of vertices such that both (v, u, x) and (u, x, y) are paths of length two. The 3-arc graph of a given graph G, X(G), is defined to have vertices the arcs of G. Two arcs uv, xy are adjacent in X(G) if and only if (v, u, x, y) is a 3-arc of G. This notion was introduced in recent studies of arc-transitive graphs. In this...
متن کاملMoore Graphs of Diameter 2 and 3
In [1], the authors prove that for k = 2, there exists unique Moore graphs of type (2, 2), (3, 2) and (7, 2). Moreover, they show that only other possible (d, 2) graph is (57, 2), but could not confirm its existence. For k = 3, the authors show that the only Moore graph is (2, 3) and it is unique. Amazingly, the existence of the (57, 2) graph remains an open problem to this day. To prove these ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1979
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700014932