• Bulletin of the Korean Mathematical Society
• /
• v.48 no.3
• /
• pp.637-646
• /
• 2011

Cho and Kim [4] and Kim [6] introduced the concept of the competition index of a digraph. Cho and Kim [4] and Akelbek and Kirkland [1] also studied the upper bound of competition indices of primitive digraphs. In this paper, we study the upper bound of competition indices of strongly connected digraphs. We also study the relation between competition index and ordinary index for a symmetric strongly connected digraph.

• Korean Journal of Mathematics
• /
• v.21 no.1
• /
• pp.55-62
• /
• 2013

The base $l(S)$ of a signed digraph S is the maximum number $k$ such that for any vertices $u$, $v$ of S, there is a pair of walks of length $k$ from $u$ to $v$ with different signs. A graph can be regarded as a digraph if we consider its edges as two-sided arcs. A signed cyclic graph $\tilde{C_n}$ is a signed digraph obtained from the cycle $C_n$ by giving signs to all arcs. In this paper, we compute the base of a signed cyclic graph $\tilde{C_n}$ when $\tilde{C_n}$ is neither symmetric nor antisymmetric. Combining with previous results, the base of all signed cyclic graphs are obtained.

• Journal of applied mathematics & informatics
• /
• v.23 no.1_2
• /
• pp.257-268
• /
• 2007

An oriented graph is a digraph with no symmetric pairs of directed arcs and without loops. The score of a vertex $v_i$ in an oriented graph D is $a_{v_i}\;(or\;simply\;a_i)=n-1+d_{v_i}^+-d_{v_i}^-,\;where\; d_{v_i}^+\;and\;d_{v_i}^-$ are the outdegree and indegree, respectively, of $v_i$ and n is the number of vertices in D. In this paper, we give a new proof of Avery's theorem and obtain some stronger inequalities for scores in oriented graphs. We also characterize strongly transitive oriented graphs.