TY  JOUR
AU1  Huang, Jing
AU2  Li, Shuchao
AU3  Wang, Hua
AB  An oriented graph
$$G^\sigma $$
G
σ
is a digraph without loops or multiple arcs whose underlying graph is G. Let
$$S\left( G^\sigma \right) $$
S
G
σ
be the skewadjacency matrix of
$$G^\sigma $$
G
σ
and
$$\alpha (G)$$
α
(
G
)
be the independence number of G. The rank of
$$S(G^\sigma )$$
S
(
G
σ
)
is called the skewrank of
$$G^\sigma $$
G
σ
, denoted by
$$sr(G^\sigma )$$
s
r
(
G
σ
)
. Wong et al. (Eur J Comb 54:76–86, 2016) studied the relationship between the skewrank of an oriented graph and the rank of its underlying graph. In this paper, the correlation involving the skewrank, the independence number, and some other parameters are considered. First we show that
$$sr(G^\sigma )+2\alpha (G)\geqslant 2V_G2d(G)$$
s
r
(
G
σ
)
+
2
α
(
G
)
⩾
2

V
G


2
d
(
G
)
, where
$$V_G$$

V
G

is the order of G and d(G) is the dimension of cycle space of G. We also obtain sharp lower bounds for
$$sr(G^\sigma )+\alpha (G),\, sr(G^\sigma )\alpha (G)$$
s
r
(
G
σ
)
+
α
(
G
)
,
s
r
(
G
σ
)

α
(
G
)
,
$$sr(G^\sigma )/\alpha (G)$$
s
r
(
G
σ
)
/
α
(
G
)
and characterize all corresponding extremal graphs.
TI  Relation between the skewrank of an oriented graph and the independence number of its underlying graph
JF  Journal of Combinatorial Optimization
DO  10.1007/s108780180282x
DA  20180330
UR  https://www.deepdyve.com/lp/springerjournals/relationbetweentheskewrankofanorientedgraphandtheVs4Koc0ou9
SP  65
EP  80
VL  36
IS  1
DP  DeepDyve