This article discusses a mixed graph called mixed hourglass graph. The adjacency of a mixed hourglass graph is coined from an hourglass matrix in which the matrix is obtained from quadratic interlocking factorization. Mixed hourglass graph is a weighted graph with loops, but replacing the weights of the graph with 1’s produce an unweighted mixed hourglass graph or simply mixed hourglass graph. Then the total number of arcs and edges and the spanning subgraph of mixed hourglass graph are examined to infer that the graph is a complete mixed graph and acyclic graph.
Topics
Clocks
REFERENCES
1.
K. H.
Rosen
and K.
Krithivasan
, Discrete mathematics and its applications
(McGraw-Hill Education
, Singa-pore
, 2015
).2.
J. M.
Harris
, J. L.
Hirst
, and M. J.
Mossinghoff
, Combinatorics and graph theory
, Vol. 2
(Springer
, (2008
).3.
B.
Mohar
, Linear Algebra and its Applications
489
, 324
–340
(2016
).4.
S.
Arumugam
, A.
Brandstdt
, T.
Nishizeki
, and K.
Thulasiraman
, Handbook of graph theory, combinatorial optimization, and algorithms
(Chapman and Hall/CRC
, (2016
).5.
C.
Adiga
, B. R.
Rakshith
, and W.
So
, Linear Algebra and its Applications
495
, 223
–241
(2016
).6.
K.
Guo
and B.
Mohar
, Journal of Graph Theory
85
, 217
–248
(2015
).7.
J.
Zhang
and H.
Kan
, Linear Algebra and its Applications
453
, 141
–153
(2014
).8.
D.
Kalita
, “Determinant of the laplacian matrix of a weighted directed graph,” in Combinatorial Matrix Theory and Generalized Inverses of Matrices
(Springer
, 2013
), pp. 57
–62
.9.
G.
Aalipour
, A.
Abiad
, Z.
Berikkyzy
, J.
Cummings
, J.
De Silva
, W.
Gao
, K.
Heysse
, L.
Hogben
, F. H.
Kenter
, and J. C.-H.
Lin
, Linear Algebra and its Applications
497
, 66
–87
(2016
).10.
M.
Beck
, D.
Blado
, J.
Crawford
, T.
Jean-Louis
, and M.
Young
, Graphs and Combinatorics
31
, 91
–98
(2015
).11.
G.
Yu
, X.
Liu
, and H.
Qu
, Applied Mathematics and Computation
293
, 287
–292
(2017
).12.
G.
Yu
and H.
Qu
, Applied Mathematics and Computation
269
, 70
–76
(2015
).13.
J.
Liu
and X.
Li
, Linear Algebra and its Applications
466
, 182
–207
(2015
).14.
J.
Caughman
, J.
Krussel
, and J.
Mahoney
, Graphs and Combinatorics
33
, 1
–13
(2017
).15.
H. L.
Bodlaender
, SIAM Journal on computing
25
, 1305
–1317
(1996
).16.
S. S.
Ray
, Graph Theory with Algorithms and Its Applications: In Applied Science and Technology
(Springer Science and Business Media
, (2012
).17.
R.
Ponraj
, S. S.
Narayanan
, and A.
Ramasamy
, Jordan J. Math. and Stat.(JJMS)
8
, 59
–77
(2015
).18.
S.
Alikhani
, J. I.
Brown
, and S.
Jahari
, Filomat
30
, 169
–178
(2016
).19.
M.
Liu
, Y.
Zhu
, H.
Shan
, and K. C.
Das
, Linear Algebra and its Applications
513
, 55
–68
(2017
).20.
O.
Babarinsa
and H.
Kamarulhaili
, “Quadrant interlocking factorization of hourglass matrix,” in AIP Con-ference Proceedings
, Vol. 1974
, edited by D.
Mohamad
(AIP Publishing
) p. 030009
.21.
C.
Demeure
, IEEE Transactions on Acoustics, Speech, and Signal Processing
37
, 1601
–1603
(1989
).22.
G.
Heinig
and K.
Rost
, “Schur-type algorithms for the solution of hermitian toeplitz systems via factoriza-tion,” in Recent advances in operator theory and its applications
(Springer
, 2005
), pp. 233
–252
.23.
O.
Babarinsa
and H.
Kamarulhaili
, Communications in Mathematics and Applications
10
, 45
–53
(2019
).
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