On the index of unbalanced signed bicyclic graphs
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DOI: 10.1007/s40314-021-01498-3
Abstract: In this paper, we focus on the index ( largest eigenvalue) of the adjacency matrix of connected signed graphs. We give some general results on the index when the corresponding signed graph is perturbed. As… read more here.
Keywords: index; bicyclic graphs; index unbalanced; unbalanced signed ... See more keywords
Regularity of bicyclic graphs and their powers
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DOI: 10.1142/s0219498820500577
Abstract: Let [Formula: see text] be the edge ideal of a bicyclic graph [Formula: see text] with a dumbbell as the base graph. In this paper, we characterize the Castelnuovo–Mumford regularity of [Formula: see text] in… read more here.
Keywords: bicyclic graphs; see text; regularity bicyclic; formula see ... See more keywords
Extremal reformulated forgotten index of trees, unicyclic and bicyclic graphs
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DOI: 10.2298/fil2401025s
Abstract: The reformulated forgotten index (RF) is the edge version of the ordinary forgotten index. We describe graph transformations, by means of which RF increases or decreases. Using these transformations, the trees, unicyclic, and bicyclic graphs… read more here.
Keywords: trees unicyclic; reformulated forgotten; forgotten index; unicyclic bicyclic ... See more keywords
Maximal hitting times for random walks on bicyclic graphs with a given number of pendant vertices
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DOI: 10.2298/fil2513507z
Abstract: Let HG (x, y) be the expected hitting time from vertex x to vertex y for the first time on a simple connected graph G and ?(G) = max,y?V(G)xG H (x, y). Lettn G be… read more here.
Keywords: maximal hitting; hitting times; pendant vertices; graphs ... See more keywords
On the Extremal Weighted Mostar Index of Bicyclic Graphs
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DOI: 10.3390/axioms13080519
Abstract: Let G be a simple connected graph with edge set E(G) and vertex set V(G). The weighted Mostar index of a graph G is defined as w+Mo(G)=∑e=uv∈E(G)(dG(u)+dG(v))|nu(e)−nv(e)|, where nu(e) denotes the number of vertices closer… read more here.
Keywords: mostar index; bicyclic graphs; extremal weighted; weighted mostar ... See more keywords