TY - JOUR
AU - Hong, Zixuan
AU - Hou, Yaoping
PY - 2023/03/20
Y2 - 2024/07/15
TI - On the Net Distance Matrix of a Signed Block Graph
JF - Contemporary Mathematics
JA - Contemp. Math.
VL - 4
IS - 1
SE - Research Article
DO - 10.37256/cm.4120232065
UR - https://ojs.wiserpub.com/index.php/CM/article/view/2065
SP - 167-181
AB - <p><span style="color: #222222;">A connected signed graph </span><span style="color: #222222;"><em>Ġ</em></span><span style="color: #222222;">, where all blocks of it are positive cliques or negative cliques (of </span><span style="color: #222222;">possibly varying sizes), is called a signed block graph. Let </span><em>A, N</em><span style="color: #222222;"> and <em>D̃</em> be adjacency, net </span>Laplacian and net distance matrices of a signed block graph, respectively. In this paper the formulas for the determinant of <em>A</em> and <em>D̃</em> were given firstly. Then the inverse (resp. Moore-Penrose inverse) of <em>D̃</em> is obtained if it is nonsingular (resp. singular), which is the sum of a Laplacian-like matrix and at most two matrices with rank 1.</p>
ER -