scholarly journals Linear Time Algorithm to Check the Singularity of Block Graphs

2019 ◽  
pp. 77-90 ◽  
Author(s):  
Ranveer Singh ◽  
Naomi Shaked-Monderer ◽  
Avi Berman
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Block Graphs

scholarly journals A linear time algorithm for metric dimension of cactus block graphs

2016 ◽  
Vol 630 ◽  
pp. 43-62 ◽  
Author(s):  
Stefan Hoffmann ◽  
Alina Elterman ◽  
Egon Wanke
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Metric Dimension ◽  
Linear Time Algorithm ◽  
Block Graphs

A linear time algorithm for the nullity of vertex-weighted block graphs

2021 ◽  
Author(s):  
Ranveer Singh ◽  
Naomi Shaked-Monderer ◽  
Avi Berman
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Block Graphs

scholarly journals A linear-time algorithm for the identifying code problem on block graphs

2017 ◽  
Vol 62 ◽  
pp. 249-254 ◽  
Author(s):  
Gabriela R. Argiroffo ◽  
Silvia M. Bianchi ◽  
Yanina Lucarini ◽  
Annegret K. Wagler
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Identifying Code ◽  
Block Graphs

scholarly journals Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 293
Author(s):  
Xinyue Liu ◽  
Huiqin Jiang ◽  
Pu Wu ◽  
Zehui Shao
Keyword(s):  
Linear Time ◽  
Minimum Weight ◽  
Domination Number ◽  
Time Algorithm ◽  
Simple Graph ◽  
Linear Time Algorithm ◽  
Domination Problem ◽  
Np Complete ◽  
Chordal Bipartite Graphs ◽  
Dominating Function

For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v)≠0 has a neighbor u with f(u)≠0 for every vertex v∈V(G). The weight of a TR3DF f is the sum f(V)=∑v∈V(G)f(v) and the minimum weight of a total Roman {3}-dominating function on G is called the total Roman {3}-domination number denoted by γt{R3}(G). In this paper, we show that the total Roman {3}-domination problem is NP-complete for planar graphs and chordal bipartite graphs. Finally, we present a linear-time algorithm to compute the value of γt{R3} for trees.

A Linear time algorithm for deciding security

1976 ◽  
Author(s):  
A. K. Jones ◽  
R. J. Lipton ◽  
L. Snyder
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm

AN IMPROVED ALGORITHM FOR FINDING TREE DECOMPOSITIONS OF SMALL WIDTH

2000 ◽  
Vol 11 (03) ◽  
pp. 365-371 ◽  
Author(s):  
LJUBOMIR PERKOVIĆ ◽  
BRUCE REED
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Tree Decomposition ◽  
Linear Time Algorithm ◽  
Input Graph ◽  
Primary Motivation ◽  
Small Width ◽  
Tree Decompositions ◽  
Improved Algorithm

We present a modification of Bodlaender's linear time algorithm that, for constant k, determine whether an input graph G has treewidth k and, if so, constructs a tree decomposition of G of width at most k. Our algorithm has the following additional feature: if G has treewidth greater than k then a subgraph G′ of G of treewidth greater than k is returned along with a tree decomposition of G′ of width at most 2k. A consequence is that the fundamental disjoint rooted paths problem can now be solved in O(n2) time. This is the primary motivation of this paper.

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