Relation between the inertia indices of a complex unit gain graph and those of its underlying graph

Vertex Metric-Based Dimension of Generalized Perimantanes Diamondoid Structure

“…Moreover its resolving set shown in the Figure 4. The locations of the full vertex set of D 1 , in regard to the elements of B f are described as ( 8) and (9), as shown at the bottom of the page. We can look over the entire vertex set of perimantanes diamondoid structure D 1 , have unique locations and fulfilling the idea of fault-tolerant resolving set, which leads to the conclusion that defined B f is one of a possible resolving set with B f = 6.…”

The number of spanning trees in a k5 chain graph

“…Graph theory is a fundamental branch of mathematics that studies the properties and relationships of graphs, which consist of vertices (nodes) connected by edges [1,2]. Graph theory, pioneered by Leonhard Euler in the 18th century, has emerged as a vital area of study in mathematics and computer science [3][4][5][6].…”

Mixed graphs with cut vertices having exactly two positive eigenvalues

“…Clearly, the complex unit gain graph is a natural generalization of a simple graph. So, the complex unit gain graph attracts much plenty of researchers' attention; see [18,24,30,31,29,34,43,55,58,61].…”

“…The spectral-based graph invariants are widely investigated in the literature, such as inertia index [9,12,15,23,39,37,42,52,44,49,56,57,61] of simple graphs, signed graphs, mixed graphs and complex unit gain graphs, nullity [3,7,6,8,10,14,38,41,45,56,57,64] of simple graphs and signed graphs, rank [1,11,46,47,48,54] of simple graphs, signed graphs and complex unit gain graphs, the H-rank [4,5,50] of mixed graphs and skew-rank [20,22,32,33,26,27,40,53,62] of oriented graphs. The spectral parameter "inertia index" can determine the structure of a graph to some extent and has attracted much attention recently.…”