Jul 2026· Journal of Algebra and its Applications· 0 citations
Abstract
Consider a group [Formula: see text] and construct its power graph, whose vertex set consists of the elements of [Formula: see text]. Two distinct vertices (elements) are adjacent in the graph if and only if one element can be expressed as an integral power of the other. In this article, we improved the bounds of the spectral radius of the power graphs of the cyclic group [Formula: see text], the dihedral group [Formula: see text], and the dicyclic group [Formula: see text]. For [Formula: see text] the power graph of the cyclic group [Formula: see text] is not a complete multipartite graph. We find the second largest eigenvalue bounds of the same with the clique number. In some cases, we find the bounds are exact if and only if they belong to a particular family of graphs. Lastly, we work on the distance spectral radius of the power graphs of the same groups
For a given positive integer [Formula: see text], the prime-[Formula: see text] graph denoted by [Formula: see text] is defined on the vertex set comprising all positive divisors of [Formula: see text] greater than 1. An edge exists between two distinct vertices [Formula: see text] and [Formula: see text] if and only i...
Graphs whose edge rings have regularity two are not completely characterized. We, therefore, study the minimal graded free resolution of edge rings of certain families of graphs, such as the general barbell graph [Formula: see text] (or [Formula: see text]-barbell graph) and the complete [Formula: see text]-sunlet grap...
Shahnawaz Ahmad Rather, S. Pirzada· Algebra Colloquium· 0 citations
Let [Formula: see text] be a graph with no isolated vertex. A dominated coloring of [Formula: see text] is a proper coloring of [Formula: see text] such that each color class is dominated by at least one vertex. The minimum number of colors needed for a dominated coloring of [Formula: see text] is called the dominated...
Let [Formula: see text] be a commutative ring, and let [Formula: see text] denote the set of all nonzero elements of [Formula: see text]. The weak zero-divisor graph of [Formula: see text], denoted by [Formula: see text], is an undirected graph whose vertex set consists of the elements in [Formula: see text]. Two disti...
Sandip Rawade, M. Nazim, C. Abdioglu et al.· Asian-European Journal of Ma...· 0 citations
The eccentricity of any vertex [Formula: see text] in a connected graph [Formula: see text] is the length of the largest distance from [Formula: see text] to any other vertex in [Formula: see text]. The eccentric graph of any graph [Formula: see text], denoted by [Formula: see text], is a graph with the same vertex set...
H. Deepika, T. A. Mangam· Journal of Interconnection N...· 0 citations
Let [Formula: see text] be a ring with unity. The idempotent graph [Formula: see text] of a ring [Formula: see text] is an undirected simple graph whose vertex set is [Formula: see text] and two vertices [Formula: see text], [Formula: see text] are adjacent if and only if [Formula: see text] is an idempotent element of...
Praveen Mathil, Jitender Kumar, Barkha Baloda· Journal of Algebra and its A...· 0 citations
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