Publications (15)
Induced subgraphs of zero-divisor graphs
G. Arunkumar, Peter J. Cameron, T. Kavaskar +1
The zero-divisor graph of a finite commutative ring with unity is the graph whose vertex set is the set of zero-divisors in the ring, with and adjacent if . We show t…
On the -vertex problem in Bipartite Graphs
G. Arunkumar, Puja Samanta
In a recent work, Sharma and Panda~\cite{sharma} showed that every bipartite graph with a perfect matching has property (P). In this paper, we investigate the converse direction, i…
On the spectrum of generalized H-join operation constrained by indexing maps -- I
R. Ganeshbabu, G. Arunkumar
Fix . A new generalization of the -join operation of a family of graphs constrained by indexing maps is introduce…
Super graphs on groups, I
G. Arunkumar, Peter J. Cameron, Rajat Kanti Nath +1
Let be a finite group. A number of graphs with the vertex set have been studied, including the power graph, enhanced power graph, and commuting graph. These graphs form a h…
The P-vertex problem for graphs with perfect matchings
G. Arunkumar, U. S. Jerisha
Sharma and Panda recently proved that every bipartite graph with a perfect matching has property (P); that is, it admits a non-singular real symmetric matrix with support graph G f…
Super graphs on groups, II
G. Arunkumar, Peter J. Cameron, Rajat Kanti Nath
In an earlier paper, the authors considered three types of graphs, and three equivalence relations, defined on a group, viz.\ the power graph, enhanced power graph, and commuting g…
Chromatic symmetric function of graphs from Borcherds algebras
G. Arunkumar
Let be a Borcherds algebra with the associated graph . We prove that the chromatic symmetric function of can be recovered from the Weyl denominator identity of…
The Peterson recurrence formula for the chromatic discriminant of a graph
G. Arunkumar
The absolute value of the coefficient of in the chromatic polynomial of a graph is known as the chromatic discriminant of and is denoted . There is a well known…
Main functions and the spectrum of super graphs
G. Arunkumar, Peter J. Cameron, R. Ganeshbabu +1
Let A be a graph type and B an equivalence relation on a group . Let be the equivalence class of with respect to the equivalence relation B. The B superA graph of …
Proper -caterpillars are distinguished by their Chromatic Symmetric Functions
G. Arunkumar, Narayanan Narayanan, Raghavendra Rao B. V. +1
Stanley's Tree Isomorphism Conjecture posits that the chromatic symmetric function can distinguish non-isomorphic trees. While already established for caterpillars and other subcla…
A generalization of Fiedler's lemma and the spectra of H-join of graphs
M. Saravanan, S. P. Murugan, G. Arunkumar
A new generalization of Fiedler's lemma is obtained by introducing the concept of the main function of a matrix. As applications, the universal spectra of the H-join, the spectra o…
Groups with maximum vertex degree commuting graphs
Sushil Bhunia, G. Arunkumar
Let be a group and be its center. We associate a commuting graph , whose vertex set is and two distinct vertices are adjacent if they commute. W…
A study on free roots of Borcherds-Kac-Moody Lie Superalgebras
Shushma Rani, G. Arunkumar
Let be a Borcherds-Kac-Moody Lie superalgebra (BKM superalgebra in short) with the associated graph . Any such is constructed from a free Lie superal…
Root multiplicities for Borcherds algebras and graph coloring
G. Arunkumar, Deniz Kus, R. Venkatesh
We establish a connection between root multiplicities for Borcherds-Kac-Moody algebras and graph coloring. We show that the generalized chromatic polynomial of the graph associated…
A note on topological indices and the twin classes of graphs
P. Gangaeswari, K. Selvakumar, G. Arunkumar
Topological indices are parameters associated with graphs that have many applications in different areas such as mathematical chemistry. Among various topological indices, the Wien…